A328153 Number of set partitions of [n] such that at least one of the block sizes is 3.

0, 0, 0, 1, 4, 20, 90, 455, 2352, 13132, 76540, 473660, 3069220, 20922330, 149021600, 1109629885, 8604815520, 69437698160, 581661169640, 5051885815603, 45411759404560, 421977921782270, 4047693372023070, 40034523497947132, 407818256494533984, 4274309903558446900

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

Formula

E.g.f.: exp(exp(x)-1) - exp(exp(x)-1-x^3/6).

a(n) = A000110(n) - A124504(n).

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(
      `if`(j=k, 0, b(n-j, k)*binomial(n-1, j-1)), j=1..n))
    end:
a:= n-> b(n, 0)-b(n, 3):
seq(a(n), n=0..27);

Mathematica

b[n_, k_] := b[n, k] = If[n==0, 1, Sum[If[j==k, 0, b[n-j, k] Binomial[n-1, j-1]], {j, 1, n}]];
a[n_] := b[n, 0] - b[n, 3];
a /@ Range[0, 27] (* Jean-François Alcover, May 02 2020, after Maple *)

Crossrefs

Column k=3 of A327884.

Cf. A000110, A124504, A328155.

Sequence in context: A180284 A065180 A229245 * A070733 A166175 A094971

Adjacent sequences: A328150 A328151 A328152 * A328154 A328155 A328156

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2019

Status

approved