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A271766 Number of set partitions of [n] with minimal block length multiplicity equal to six. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=6 of A271424.

Sequence in context: A035912 A226599 A305332 * A104439 A290035 A289954

Adjacent sequences:  A271763 A271764 A271765 * A271767 A271768 A271769

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified November 21 03:20 EST 2018. Contains 317427 sequences. (Running on oeis4.)