Triangles Row Sum Bell

Triangles whose row sums are the Bell numbers and having at least one diagonal equal to the Bell numbers

A056857 Triangle read by rows: T(n,c) = number of successive equalities in set partitions of n.

A056860 Triangle T(n,k) = number of element-subset partitions of {1..n} with n-k+1 equalities (n >= 1, 1<=k<=n).

A095149 Triangle read by rows: Aitken's array (A011971) but with a leading diagonal before it given by the Bell numbers (A000110), 1, 1, 2, 5, 15, 52, ...

A113547 Triangle read by rows: number of labeled partitions of n with maximin m.

A133611 A triangular array of numbers related to factorization and number of parts in Murasaki diagrams.

A152431 Eigentriangle, row sums = A000110, the Bell numbers.

A188792 Table with T(n,k) the number of word structures of length n which can be decomposed into k palindromes but not fewer.

A212431 Triangle read by rows: row sums, right and left borders are the Bell sequence, or a shifted variant. See Comments for precise definition.

A259691 Triangle read by rows, another version of A056857.

A259697 Triangle read by rows: T(n,k) = number of rook patterns on n X n board where bottom rook is in column k.

Triangles whose row sums are the Bell numbers

A008277 Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.

A008278 Triangle of Stirling numbers of 2nd kind, S(n,n-k+1), n >= 1, 1<=k<=n.

A048993 Triangle of Stirling numbers of 2nd kind, S(n,k), n >= 0, 0<=k<=n.

A056857 Triangle read by rows: T(n,c) = number of successive equalities in set partitions of n.

A056858 Triangle of number of rises in restricted growth strings (RGS) for the set partitions of n.

A056859 Triangle of number of falls in set partitions of n.

A056860 Triangle T(n,k) = number of element-subset partitions of {1..n} with n-k+1 equalities (n >= 1, 1<=k<=n).

A069138 Triangle formed by multiplying Stirling numbers of 2nd kind S2(n,m) (A008277) by m+1.

A080417 Signed Stirling numbers of the second kind.

A080510 Triangle read by rows: T(n,k) gives the number of set partitions of {1,...,n} with maximum block length k.

A085791 Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,0,1,1,1,2,1,3,1,4,1,5,...], where DELTA is the operator defined in A084938.

A095149 Triangle read by rows: Aitken's array (A011971) but with a leading diagonal before it given by the Bell numbers (A000110), 1, 1, 2, 5, 15, 52, ...

A095675 Triangle read by rows, formed from product of Aitken's (or Bell's) triangle (A011971) and Pascal's triangle (A007318).

A106800 Triangle of Stirling numbers of 2nd kind, S(n,n-k), n >= 0, 0<=k<=n.

A113547 Triangle read by rows: number of labeled partitions of n with maximin m.

A124321 Triangle read by rows: T(n,k) is the number of set partitions of {1,2,...,n} (or of any n-set) having k blocks of odd size (0<=k<=n).

A124323 Triangle read by rows: T(n,k) is the number of partitions of an n-set having k singleton blocks (0<=k<=n).

A124424 Triangle read by rows: T(n,k) is the number of partitions of the set {1,2,...,n}, having exactly k blocks consisting of entries of the same parity (0<=k<=n).

A124496 Triangle read by rows: T(n,k) is the number of set partitions of {1,2,...,n} in which the size of the last block is k, 1<=k<=n; the blocks are ordered with increasing least elements.

A127743 Triangular array where T(n,k) is the number of set partitions of n with k atomic parts.

A130167 Another version of triangle in A127743 .

A133611 A triangular array of numbers related to factorization and number of parts in Murasaki diagrams.

A136790 Triangle read by rows: A011971 * A007318^(-1).

A143397 Triangle T(n,k)=number of forests of labeled rooted trees of height at most 1, with n labels and k nodes, where any root may contain >= 1 labels, n >= 0, 0<=k<=n.

A151510 The triangle in A151338 read by rows upwards.

A151511 The triangle in A151359 read by rows downwards.

A151512 The triangle in A151359 read by rows upwards.

A152431 Eigentriangle, row sums = A000110, the Bell numbers.

A154109 Convolution triangle by rows, A004736 * (A154108 * 0^n-k)); row sums = Bell numbers.

A154959 Triangle read by rows. Signed version of A008277.

A177254 Triangle read by rows: T(n,k) is the number of partitions of the set {1,2,...,n} having k adjacent blocks (0 <= k <= n). An adjacent block is a block of the form (i, i+1, i+2, ...).

A178979 Triangular array read by rows: T(n,k) is the number of set partitions of {1,2,...,n} in which the shortest block has length k (1<=k<=n).

A185982 Triangle read by rows: number of set partitions of n elements with k connectors, 0<=k<n.

A185983 Triangle read by rows: number of set partitions of n elements with k circular connectors.

A188792 Table with T(n,k) the number of word structures of length n which can be decomposed into k palindromes but not fewer.

A212431 Triangle read by rows: row sums, right and left borders are the Bell sequence, or a shifted variant. See Comments for precise definition.

A213735 Triangle read by rows: row n is the expansion of x^n in terms of (x+k)!/x! for decreasing k.

A250104 Triangle read by rows: T(n,k) = number of partitions of n with k circular successions (n>=0, 0 <= k <= n).

A256549 Triangle read by rows, T(n,k) = {n,k}*h(k), where {n,k} are the Stirling set numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.

A259691 Triangle read by rows, another version of A056857.

A259697 Triangle read by rows: T(n,k) = number of rook patterns on n X n board where bottom rook is in column k.

A261780 Number A(n,k) of compositions of n where each part i is marked with a word of length i over a k-ary alphabet whose letters appear in alphabetical order; square array A(n,k), n>=0, k>=0, read by antidiagonals.

A271423 Number T(n,k) of set partitions of [n] with maximal block length multiplicity equal to k; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

A271424 Number T(n,k) of set partitions of [n] with minimal block length multiplicity equal to k; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

A271466 Number T(n,k) of set partitions of [n] such that k is the largest element of the last block; triangle T(n,k), n>=1, 1<=k<=n, read by rows.