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

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=10 of A292745.

Programs

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 *)