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A271765 Number of set partitions of [n] with minimal block length multiplicity equal to five. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A271424.

Sequence in context: A260136 A215838 A145493 * A133814 A104438 A125013

Adjacent sequences:  A271762 A271763 A271764 * A271766 A271767 A271768

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified November 13 10:50 EST 2019. Contains 329093 sequences. (Running on oeis4.)