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%I #25 Dec 10 2017 03:54:25
%S 1,1,2,2,3,4,5,7,8,10,12,14,18,20,25,29,34,40,45,53,60,69,80,89,103,
%T 114,131,147,165,186,207,232,258,286,319,352,392,432,477,525,578,636,
%U 699,765,839,916,1002,1093,1192,1298,1413,1536,1671,1810,1965,2126,2304
%N Number of partitions of n into generalized pentagonal numbers.
%H Seiichi Manyama, <a href="/A095699/b095699.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)
%F G.f.: 1/Product_{k>=1} (1-x^(k*(3*k-1)/2))*(1-x^(k*(3*k+1)/2)).
%t nmax = 100; CoefficientList[Series[1/Product[(1-x^(k*(3*k-1)/2)) * (1-x^(k*(3*k+1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 10 2017 *)
%o (PARI)
%o b(n) = (3*n^2 + 2*n + (n%2) * (2*n + 1)) / 8; \\ A001318
%o N=66; x='x+O('x^N);
%o Vec(1/prod(k=1,N, (1-x^b(k))) )
%o \\ _Joerg Arndt_, Oct 13 2014
%Y Cf. A001318, A218379, A290942.
%K nonn
%O 0,3
%A _Jon Perry_, Jul 06 2004
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