A320741 Number of partitions of n with ten sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 20, 63, 233, 966, 4454, 22404, 121616, 706361, 4361910, 28491982, 196018395, 1414922459, 10677120529, 83924901635, 684582037213, 5772723290503, 50123602905429, 446382776341382, 4062023996661972, 37638652689027910, 354017801203414670

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1006

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..10), add(b(n-i*j, i-1), j=0..n/i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 10}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Column k=10 of A292745.

Sequence in context: A320738 A320739 A320740 * A292503 A340357 A071688

Adjacent sequences: A320738 A320739 A320740 * A320742 A320743 A320744

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved