A271767 Number of set partitions of [n] with minimal block length multiplicity equal to seven.

1, 0, 0, 0, 0, 0, 0, 135135, 0, 0, 0, 0, 0, 0, 51925673800, 43212118950, 607370338575, 265034329560, 17166996346500, 1305093289500, 584129638842750, 56071685084790375, 176898040019801100, 518112685551586125, 26529011711988035250, 4672320885518286000

Offset

7,8

Links

Alois P. Heinz, Table of n, a(n) for n = 7..577

Wikipedia, Partition of a set

Formula

a(n) = A271424(n,7):

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, 7)-b(n$2, 8):
seq(a(n), n=7..35);

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, 7] - b[n, n, 8];
Table[a[n], {n, 7, 35}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=7 of A271424.

Sequence in context: A151940 A270896 A353031 * A104440 A290036 A289955

Adjacent sequences: A271764 A271765 A271766 * A271768 A271769 A271770

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved