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A328153 Number of set partitions of [n] such that at least one of the block sizes is 3. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 26 06:08 EDT 2021. Contains 348257 sequences. (Running on oeis4.)