A320822 Number of partitions of n with exactly nine sorts of part 1 which are introduced in ascending order.

1, 45, 1156, 22321, 360704, 5158652, 67512671, 826325926, 9601854284, 107074391802, 1155110296163, 12128784832510, 124544257464575, 1255354199998891, 12457896065009874, 122014591067156240, 1181759128040203056, 11337243349606910986, 107879491494316487583

Offset: 9

Author

Alois P. Heinz, Oct 21 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..1053

Crossrefs

Column k=9 of A292746.

Cf. A320739, A320740.

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))(9):
seq(a(n), n=9..35);

Formula

a(n) = A320740(n) - A320739(n).