A144351 Lower triangular array called S1hat(1) related to partition number array A107106.

1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 24, 8, 3, 1, 1, 120, 34, 9, 3, 1, 1, 720, 156, 36, 9, 3, 1, 1, 5040, 924, 166, 37, 9, 3, 1, 1, 40320, 6144, 968, 168, 37, 9, 3, 1, 1, 362880, 48096, 6372, 978, 169, 37, 9, 3, 1, 1, 3628800, 420480, 49368, 6416, 980, 169, 37, 9, 3, 1, 1, 39916800, 4134240

Offset

1,4

Comments

If in the partition array M31hat(1):=A107106 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(1). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

The first three columns are A000142(n-1) (factorials), A024419 (guess), A144352.

Links

Table of n, a(n) for n=1..68.

W. Lang, First 10 rows of the array and more.

W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3.

Formula

a(n,m)=sum(product(|S1(1;j,1)|^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S1(1,n,1)|= |A008275(n,1)| = A000142(n-1) = (n-1)!.

Example

[1];[1,1];[2,1,1];[6,3,1,1];[24,8,3,1,1];...

Crossrefs

Row sums A107107.

A134134 (S1hat(2)= S2'(2)).

Sequence in context: A120258 A201922 A181644 * A213936 A142589 A284308

Adjacent sequences: A144348 A144349 A144350 * A144352 A144353 A144354

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 09 2008

Status

approved