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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
OFFSET
8,9
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved