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

0,2

Links

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

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

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);

Crossrefs

Column k=8 of A292622.

Sequence in context: A171442 A341402 A247541 * A093809 A244244 A037157

Adjacent sequences: A320692 A320693 A320694 * A320696 A320697 A320698

Keyword

nonn

Author

Alois P. Heinz, Oct 19 2018

Status

approved