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A271767 Number of set partitions of [n] with minimal block length multiplicity equal to seven. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A133528 A151940 A270896 * A104440 A290036 A289955

Adjacent sequences:  A271764 A271765 A271766 * A271768 A271769 A271770

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified October 25 22:20 EDT 2021. Contains 348256 sequences. (Running on oeis4.)