cp's OEIS Frontend

A320694 Number of partitions of n with up to seven distinct kinds of 1.

%I A320694 #10 Apr 24 2021 20:44:25
%S A320694 1,7,22,43,65,93,137,201,287,401,552,751,1010,1344,1774,2323,3017,
%T A320694 3893,4995,6370,8078,10195,12809,16023,19958,24761,30613,37720,46317,
%U A320694 56693,69192,84207,102200,123715,149384,179947,216265,259338,310333,370593,441667
%N A320694 Number of partitions of n with up to seven distinct kinds of 1.
%H A320694 Alois P. Heinz, <a href="/A320694/b320694.txt">Table of n, a(n) for n = 0..10000</a>
%F A320694 a(n) ~ Pi * 2^(9/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - _Vaclav Kotesovec_, Oct 24 2018
%F A320694 G.f.: (1 + x)^7 * Product_{k>=2} 1 / (1 - x^k). - _Ilya Gutkovskiy_, Apr 24 2021
%p A320694 b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p A320694       binomial(7, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
%p A320694     end:
%p A320694 a:= n-> b(n$2):
%p A320694 seq(a(n), n=0..60);
%Y A320694 Column k=7 of A292622.
%K A320694 nonn
%O A320694 0,2
%A A320694 _Alois P. Heinz_, Oct 19 2018