A325478 Number of colored set partitions of [n] where colors of the elements of subsets are distinct and in increasing order and all colors of an initial interval of the color palette are used.

1, 1, 4, 29, 329, 5252, 110955, 2972769, 97922354, 3872594811, 180459028989, 9759149087646, 604841170643957, 42508077480226893, 3357224252026104140, 295651782273190911233, 28834727303442640011901, 3095877335697619795977036, 363977673792652615285223095

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..296

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)*
      binomial(n-1, j-1)*binomial(k, j), j=1..min(k, n)))
    end:
a:= n-> add(add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k), k=0..n):
seq(a(n), n=0..23);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k] Binomial[n - 1, j - 1] Binomial[k, j], {j, 1, Min[k, n]}]];
a[n_] := Sum[Sum[b[n, k - i] (-1)^i Binomial[k, i], {i, 0, k}], {k, 0, n}];
a /@ Range[0, 23] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Crossrefs

Row sums of A322670.

Sequence in context: A295237 A028853 A118795 * A099700 A305636 A276728

Adjacent sequences: A325475 A325476 A325477 * A325479 A325480 A325481

Keyword

nonn

Author

Alois P. Heinz, Sep 06 2019

Status

approved