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A327504
Number of set partitions of [n] where each subset is again partitioned into three nonempty subsets.
11
1, 0, 0, 1, 6, 25, 100, 511, 3626, 29765, 250200, 2146771, 19575446, 195336505, 2124840900, 24646324431, 299803782466, 3809251939245, 50698296967600, 708349718638891, 10372758309704686, 158546862369781985, 2519789706502636700, 41545703617137280551
OFFSET
0,5
LINKS
FORMULA
E.g.f.: exp((exp(x)-1)^3/3!).
a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling2(n,3*k)/(6^k * k!). - Seiichi Manyama, May 07 2022
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
*binomial(n-1, j-1)*Stirling2(j, 3), j=3..n))
end:
seq(a(n), n=0..25);
MATHEMATICA
a[n_] := a[n] = If[n == 0, 1, Sum[a[n - j] Binomial[n - 1, j -1] StirlingS2[j, 3], {j, 3, n}]];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)
PROG
(PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 2)/(6^k*k!)); \\ Seiichi Manyama, May 07 2022
CROSSREFS
Column k=3 of A324162.
Cf. A346894.
Sequence in context: A034559 A034347 A009121 * A346390 A323824 A037537
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 14 2019
STATUS
approved