cp's OEIS Frontend

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

%I A320695 #10 Apr 24 2021 20:44:30
%S A320695 1,8,29,65,108,158,230,338,488,688,953,1303,1761,2354,3118,4097,5340,
%T A320695 6910,8888,11365,14448,18273,23004,28832,35981,44719,55374,68333,
%U A320695 84037,103010,125885,153399,186407,225915,273099,329331,396212,475603,569671,680926
%N A320695 Number of partitions of n with up to eight distinct kinds of 1.
%H A320695 Alois P. Heinz, <a href="/A320695/b320695.txt">Table of n, a(n) for n = 0..10000</a>
%F A320695 a(n) ~ Pi * 2^(11/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - _Vaclav Kotesovec_, Oct 24 2018
%F A320695 G.f.: (1 + x)^8 * Product_{k>=2} 1 / (1 - x^k). - _Ilya Gutkovskiy_, Apr 24 2021
%p A320695 b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p A320695       binomial(8, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
%p A320695     end:
%p A320695 a:= n-> b(n$2):
%p A320695 seq(a(n), n=0..60);
%Y A320695 Column k=8 of A292622.
%K A320695 nonn
%O A320695 0,2
%A A320695 _Alois P. Heinz_, Oct 19 2018