A271768 Number of set partitions of [n] with minimal block length multiplicity equal to eight.

1, 0, 0, 0, 0, 0, 0, 0, 2027025, 0, 0, 0, 0, 0, 0, 0, 10652498631775, 4141161399375, 64602117830250, 26428139112375, 2096632369581750, 137561852302875, 80768458994973750, 609202488769875, 158980016052580597875, 353341814230502847750, 1344898884799733513250

Offset

8,9

Links

Alois P. Heinz, Table of n, a(n) for n = 8..578

Wikipedia, Partition of a set

Formula

a(n) = A271424(n,8).

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, 8)-b(n$2, 9):
seq(a(n), n=8..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, 8] - b[n, n, 9];
Table[a[n], {n, 8, 35}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=8 of A271424.

Sequence in context: A345086 A345085 A032754 * A104441 A346515 A290037

Adjacent sequences: A271765 A271766 A271767 * A271769 A271770 A271771

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved