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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
OFFSET
0,5
LINKS
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.
Sequence in context: A180284 A065180 A229245 * A070733 A166175 A094971
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2019
STATUS
approved