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A328155 Number of set partitions of [n] with distinct block sizes and one of the block sizes is 3. 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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 28 02:07 EDT 2021. Contains 348307 sequences. (Running on oeis4.)