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A320697 Number of partitions of n with up to ten distinct kinds of 1.

%I A320697 #10 Apr 24 2021 20:44:41
%S A320697 1,10,46,131,267,439,654,956,1394,2002,2817,3897,5320,7179,9587,12687,
%T A320697 16652,21687,28048,36051,46066,58534,73998,93113,116649,145513,180793,
%U A320697 223800,276077,339417,415942,508179,619090,752128,911336,1101444,1327973,1597358
%N A320697 Number of partitions of n with up to ten distinct kinds of 1.
%H A320697 Alois P. Heinz, <a href="/A320697/b320697.txt">Table of n, a(n) for n = 0..10000</a>
%F A320697 a(n) ~ Pi * 2^(15/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - _Vaclav Kotesovec_, Oct 24 2018
%F A320697 G.f.: (1 + x)^10 * Product_{k>=2} 1 / (1 - x^k). - _Ilya Gutkovskiy_, Apr 24 2021
%p A320697 b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p A320697       binomial(10, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
%p A320697     end:
%p A320697 a:= n-> b(n$2):
%p A320697 seq(a(n), n=0..60);
%Y A320697 Column k=10 of A292622.
%K A320697 nonn
%O A320697 0,2
%A A320697 _Alois P. Heinz_, Oct 19 2018