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A271763 Number of set partitions of [n] with minimal block length multiplicity equal to three. 2
1, 0, 0, 15, 0, 0, 1540, 3150, 24255, 81235, 496210, 605605, 36987951, 13833820, 849333940, 24419945732, 111237098546, 1219799147204, 16146398449224, 109697049177254, 1037441240056529, 9042707959752775, 84237798887033660, 614681985047225810 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..576

Wikipedia, Partition of a set

FORMULA

a(n) = A271424(n,3).

EXAMPLE

a(6) = 15: 12|34|56, 12|35|46, 12|36|45, 13|24|56, 13|25|46, 13|26|45, 14|23|56, 15|23|46, 16|23|45, 14|25|36, 14|26|35, 15|24|36, 16|24|35, 15|26|34, 16|25|34.

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, $k..n/i})))

    end:

a:= n-> b(n$2, 3)-b(n$2, 4):

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, Join[{0}, Range[k, n/i]]}]]];

a[n_] := b[n, n, 3] - b[n, n, 4];

Table[a[n], {n, 3, 30}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=3 of A271424.

Sequence in context: A185294 A287285 A106239 * A271339 A202857 A055965

Adjacent sequences:  A271760 A271761 A271762 * A271764 A271765 A271766

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified November 18 16:10 EST 2018. Contains 317323 sequences. (Running on oeis4.)