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A324238 Number of set partitions of [n] where all subsets are partitioned into the same number of nonempty subsets. 2
1, 1, 3, 9, 32, 133, 625, 3328, 20172, 137073, 1023610, 8327069, 73711863, 707141074, 7278630390, 79522233635, 916354807657, 11119419230485, 142082222254701, 1908850117706652, 26862951637197372, 394233330125117457, 6013602782397882264, 95208871146458467659 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

Wikipedia, Partition of a set

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1, `if`(k=0 or k>n, 0,

add(b(n-j, k)*binomial(n-1, j-1)*Stirling2(j, k), j=k..n)))

end:

a:= n-> add(b(n, k), k=0..n):

seq(a(n), n=0..23);

MATHEMATICA

b[n_, k_] := b[n, k] = If[n == 0, 1, If[k == 0 || k > n, 0, Sum[b[n-j, k]* Binomial[n - 1, j - 1] StirlingS2[j, k], {j, k, n}]]];

a[n_] := Sum[b[n, k], {k, 0, n}];

a /@ Range[0, 23] (* Jean-François Alcover, May 05 2020, after Maple *)

CROSSREFS

Row sums of A324162.

Sequence in context: A183425 A039628 A194530 * A005964 A246138 A129416

Adjacent sequences: A324235 A324236 A324237 * A324239 A324240 A324241

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 02 2019

STATUS

approved

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Last modified February 4 13:47 EST 2023. Contains 360055 sequences. (Running on oeis4.)