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A271770 Number of set partitions of [n] with minimal block length multiplicity equal to ten. 2
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 654729075, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1228555090548911125, 55437426478058625, 1034831960923761000, 375268733082243000, 42378561928787584500, 2126522820799377000, 2014348742002209863250, 10413707343032243250 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,11

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..578

Wikipedia, Partition of a set

FORMULA

a(n) = A271424(n,10).

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, 10)-b(n$2, 11):

seq(a(n), n=10..40);

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, 10] - b[n, n, 11];

Table[a[n], {n, 10, 40}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=10 of A271424.

Sequence in context: A105382 A032432 A307759 * A290039 A289958 A263894

Adjacent sequences:  A271767 A271768 A271769 * A271771 A271772 A271773

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified October 19 20:01 EDT 2021. Contains 348091 sequences. (Running on oeis4.)