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A271768 Number of set partitions of [n] with minimal block length multiplicity equal to eight. 2
1, 0, 0, 0, 0, 0, 0, 0, 2027025, 0, 0, 0, 0, 0, 0, 0, 10652498631775, 4141161399375, 64602117830250, 26428139112375, 2096632369581750, 137561852302875, 80768458994973750, 609202488769875, 158980016052580597875, 353341814230502847750, 1344898884799733513250 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,9

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..578

Wikipedia, Partition of a set

FORMULA

a(n) = A271424(n,8).

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

seq(a(n), n=8..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, 8] - b[n, n, 9];

Table[a[n], {n, 8, 35}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=8 of A271424.

Sequence in context: A345086 A345085 A032754 * A104441 A346515 A290037

Adjacent sequences:  A271765 A271766 A271767 * A271769 A271770 A271771

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified December 2 11:44 EST 2021. Contains 349440 sequences. (Running on oeis4.)