A320739 Number of partitions of n with eight sorts of part 1 which are introduced in ascending order.

1, 1, 3, 7, 20, 63, 233, 966, 4454, 22403, 121570, 705150, 4337883, 28091897, 190105229, 1334705996, 9656244012, 71551215515, 540187472767, 4137336876098, 32036946594336, 250131019258467, 1965050543015106, 15509209887539395, 122829846706462146

Offset: 0

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1112

Crossrefs

Column k=8 of A292745.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..8), 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, 8}], 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 *)