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A320696 Number of partitions of n with up to nine distinct kinds of 1.

%I A320696 #10 Apr 24 2021 20:44:36
%S A320696 1,9,37,94,173,266,388,568,826,1176,1641,2256,3064,4115,5472,7215,
%T A320696 9437,12250,15798,20253,25813,32721,41277,51836,64813,80700,100093,
%U A320696 123707,152370,187047,228895,279284,339806,412322,499014,602430,725543,871815,1045274
%N A320696 Number of partitions of n with up to nine distinct kinds of 1.
%H A320696 Alois P. Heinz, <a href="/A320696/b320696.txt">Table of n, a(n) for n = 0..10000</a>
%F A320696 a(n) ~ Pi * 2^(13/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - _Vaclav Kotesovec_, Oct 24 2018
%F A320696 G.f.: (1 + x)^9 * Product_{k>=2} 1 / (1 - x^k). - _Ilya Gutkovskiy_, Apr 24 2021
%p A320696 b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p A320696       binomial(9, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
%p A320696     end:
%p A320696 a:= n-> b(n$2):
%p A320696 seq(a(n), n=0..60);
%Y A320696 Column k=9 of A292622.
%K A320696 nonn
%O A320696 0,2
%A A320696 _Alois P. Heinz_, Oct 19 2018