A320740 Number of partitions of n with nine sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 20, 63, 233, 966, 4454, 22404, 121615, 706306, 4360204, 28452601, 195263881, 1402218667, 10482569938, 81153069799, 647261864569, 5292447172261, 44165731426846, 374675276723042, 3220404743013997, 27967105952549269, 244844437773618386

Offset: 0

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1053

Crossrefs

Column k=9 of A292745.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..9), 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, 9}], 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 *)