A271763 Number of set partitions of [n] with minimal block length multiplicity equal to three.

1, 0, 0, 15, 0, 0, 1540, 3150, 24255, 81235, 496210, 605605, 36987951, 13833820, 849333940, 24419945732, 111237098546, 1219799147204, 16146398449224, 109697049177254, 1037441240056529, 9042707959752775, 84237798887033660, 614681985047225810

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-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=3 of A271424.

Sequence in context: A324677 A324675 A106239 * A362267 A271339 A202857

Adjacent sequences: A271760 A271761 A271762 * A271764 A271765 A271766

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved