A328155 Number of set partitions of [n] with distinct block sizes and one of the block sizes is 3.

0, 0, 0, 1, 4, 10, 60, 35, 336, 1848, 16080, 33825, 93280, 539396, 3856216, 49390250, 147478800, 708041160, 2354289744, 18196716309, 150847235040, 2615953578700, 9488756856040, 57565330671310, 296745669669768, 1435526275752900, 12231628020365000

Offset: 0

Author

Alois P. Heinz, Oct 05 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..697
• Wikipedia, Multinomial coefficients
• Wikipedia, Partition (number theory)
• Wikipedia, Partition of a set

Crossrefs

Column k=3 of A327869.

Cf. A328153.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(i*(i+1)/2 b(n$2, 0)-b(n$2, 3):
seq(a(n), n=0..29);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[i(i+1)/2 < n, 0, If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] + If[i == k, 0, b[n - i, Min[n - i, i - 1], k]*Binomial[n, i]]]];
a[n_] := b[n, n, 0] - b[n, n, 3];
a /@ Range[0, 29] (* Jean-François Alcover, May 04 2020, after Maple *)