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A271732 Number of set partitions of [n] with maximal block length multiplicity equal to three. 2
1, 0, 10, 35, 245, 1036, 4984, 37990, 242330, 1387595, 10324457, 73271562, 550531436, 3836993356, 32056517432, 271603606580, 2249464283038, 18909114389770, 173349802631034, 1639551357457112, 15220220305707538, 147729311772991971, 1423109890697311335 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

COMMENTS

At least one block length occurs exactly 3 times, and all block lengths occur at most 3 times.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..626

Wikipedia, Partition of a set

MAPLE

with(combinat):

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

      `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)

        *b(n-i*j, i-1, k)/j!, j=0..min(k, n/i))))

    end:

a:= n-> b(n$2, 3)-b(n$2, 2):

seq(a(n), n=3..30);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, 0, Min[k, n/i] }]]];

a[n_] := b[n, n, 3] - b[n, n, 2];

Table[a[n], {n, 3, 30}] (* Jean-Fran├žois Alcover, May 08 2018, after Alois P. Heinz *)

CROSSREFS

Column k=3 of A271423.

Sequence in context: A195269 A070755 A126995 * A219295 A000820 A126249

Adjacent sequences:  A271729 A271730 A271731 * A271733 A271734 A271735

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified October 27 00:02 EDT 2021. Contains 348270 sequences. (Running on oeis4.)