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A271769 Number of set partitions of [n] with minimal block length multiplicity equal to nine. 2
1, 0, 0, 0, 0, 0, 0, 0, 0, 34459425, 0, 0, 0, 0, 0, 0, 0, 0, 3139051466175625, 452214824811750, 7749317679728625, 2980506799895625, 284294494759275000, 16245399700530000, 12231973704514063500, 75947243599977750, 558368602431954063750, 668351312267239068593125 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,10

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..578

Wikipedia, Partition of a set

FORMULA

a(n) = A271424(n,9).

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

seq(a(n), n=9..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, 9] - b[n, n, 10];

Table[a[n], {n, 9, 40}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=9 of A271424.

Sequence in context: A205943 A232636 A172687 * A290038 A289957 A263893

Adjacent sequences:  A271766 A271767 A271768 * A271770 A271771 A271772

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified November 18 01:17 EST 2018. Contains 317279 sequences. (Running on oeis4.)