A271765 Number of set partitions of [n] with minimal block length multiplicity equal to five.

1, 0, 0, 0, 0, 945, 0, 0, 0, 0, 4239235, 7567560, 82702620, 41351310, 1658646990, 24448068645, 117626817945, 239611442070, 8260908743395, 1834189492520, 4508736346382576, 2979073800027325, 256635727575051825, 2371542394294648575, 16374593589666387075

Offset

5,6

Links

Alois P. Heinz, Table of n, a(n) for n = 5..577

Wikipedia, Partition of a set

Formula

a(n) = A271424(n,5).

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, 5)-b(n$2, 6):
seq(a(n), n=5..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, 5] - b[n, n, 6];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=5 of A271424.

Sequence in context: A260136 A215838 A145493 * A343330 A133814 A104438

Adjacent sequences: A271762 A271763 A271764 * A271766 A271767 A271768

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved