A271739 Number of set partitions of [n] with maximal block length multiplicity equal to ten.

1, 0, 66, 286, 4004, 33033, 328328, 3150576, 31286970, 316394650, 3928974907, 48404715723, 526502083107, 6475762500130, 88834932638892, 1136875206056150, 14448572171583550, 197345257083676845, 2738327374576989195, 37603158111513714720, 528367079280330690400

Offset

10,3

Comments

At least one block length occurs exactly 10 times, and all block lengths occur at most 10 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 10..584

Wikipedia, Partition of a set

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..min(k, n/i))))
    end:
a:= n-> b(n$2, 10)-b(n$2, 9):
seq(a(n), n=10..30);

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, 0, Min[k, n/i] }]]];
a[n_] := b[n, n, 10] - b[n, n, 9];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=10 of A271423.

Sequence in context: A322768 A158070 A242726 * A251055 A251048 A259292

Adjacent sequences: A271736 A271737 A271738 * A271740 A271741 A271742

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved