A271769 Number of set partitions of [n] with minimal block length multiplicity equal to nine.

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

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-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=9 of A271424.

Sequence in context: A363295 A172687 A332388 * A290038 A289957 A263893

Adjacent sequences: A271766 A271767 A271768 * A271770 A271771 A271772

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved