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A095699 Number of partitions of n into generalized pentagonal numbers. 8

%I

%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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Last modified February 26 20:23 EST 2020. Contains 332295 sequences. (Running on oeis4.)