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A271767
Number of set partitions of [n] with minimal block length multiplicity equal to seven.
2
1, 0, 0, 0, 0, 0, 0, 135135, 0, 0, 0, 0, 0, 0, 51925673800, 43212118950, 607370338575, 265034329560, 17166996346500, 1305093289500, 584129638842750, 56071685084790375, 176898040019801100, 518112685551586125, 26529011711988035250, 4672320885518286000
OFFSET
7,8
LINKS
FORMULA
a(n) = A271424(n,7):
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, 7)-b(n$2, 8):
seq(a(n), n=7..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, 7] - b[n, n, 8];
Table[a[n], {n, 7, 35}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)
CROSSREFS
Column k=7 of A271424.
Sequence in context: A151940 A270896 A353031 * A104440 A290036 A289955
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved