A320695 Number of partitions of n with up to eight distinct kinds of 1.

1, 8, 29, 65, 108, 158, 230, 338, 488, 688, 953, 1303, 1761, 2354, 3118, 4097, 5340, 6910, 8888, 11365, 14448, 18273, 23004, 28832, 35981, 44719, 55374, 68333, 84037, 103010, 125885, 153399, 186407, 225915, 273099, 329331, 396212, 475603, 569671, 680926

Offset: 0

Author

Alois P. Heinz, Oct 19 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=8 of A292622.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1,
      binomial(8, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);

Formula

a(n) ~ Pi * 2^(11/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018

G.f.: (1 + x)^8 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021