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

0,5

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

Maple

b:= proc(n, i, k) option remember; `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))))
    end:
a:= n-> 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 *)

Crossrefs

Column k=3 of A327869.

Cf. A328153.

Sequence in context: A092190 A328036 A222675 * A209030 A220824 A124724

Adjacent sequences: A328152 A328153 A328154 * A328156 A328157 A328158

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2019

Status

approved