A271766 Number of set partitions of [n] with minimal block length multiplicity equal to six.

1, 0, 0, 0, 0, 0, 10395, 0, 0, 0, 0, 0, 383563180, 523783260, 6547290750, 3055402350, 157964301495, 14054850810, 34828180582195, 91670862398500, 448593283888750, 11612610774464700, 7681370284312725, 6594450798260325, 179804372693675480751, 11896760875264765500

Offset

6,7

Links

Alois P. Heinz, Table of n, a(n) for n = 6..577

Wikipedia, Partition of a set

Formula

a(n) = A271424(n,6).

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, 6)-b(n$2, 7):
seq(a(n), n=6..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, 6] - b[n, n, 7];
Table[a[n], {n, 6, 30}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=6 of A271424.

Sequence in context: A226599 A374272 A305332 * A104439 A290035 A289954

Adjacent sequences: A271763 A271764 A271765 * A271767 A271768 A271769

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved