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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
OFFSET
9,10
LINKS
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-François Alcover, May 15 2018, after Alois P. Heinz *)
CROSSREFS
Column k=9 of A271424.
Sequence in context: A363295 A172687 A332388 * A290038 A289957 A263893
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved