A320821 Number of partitions of n with exactly eight sorts of part 1 which are introduced in ascending order.

1, 36, 751, 11917, 159815, 1912316, 21084803, 218711887, 2164920950, 20657703246, 191440769945, 1732792167043, 15385193971985, 134455882817716, 1159708265019855, 9893526482067374, 83627808435796896, 701411197245083482, 5844301347854288709, 48423747013469923303

Offset: 8

Author

Alois P. Heinz, Oct 21 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1112

Crossrefs

Column k=8 of A292746.

Cf. A320738, A320739.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
    end:
a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(8):
seq(a(n), n=8..35);

Formula

a(n) = A320739(n) - A320738(n).