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A327851 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A111374.

%I A327851 #22 Sep 29 2019 20:21:59
%S A327851 1,1,2,2,4,4,6,8,12,15,19,24,30,36,47,57,74,88,112,130,160,190,232,
%T A327851 277,333,399,471,554,656,768,908,1060,1256,1452,1702,1968,2294,2646,
%U A327851 3068,3549,4093,4710,5418,6211,7121,8138,9331,10625,12150,13817,15749,17858,20290,23000,26054
%N A327851 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A111374.
%C A327851 a(n) > 0.
%H A327851 Seiichi Manyama, <a href="/A327851/b327851.txt">Table of n, a(n) for n = 0..1000</a>
%F A327851 G.f.: Product_{i>=1} Product_{j>=1} (1-x^(i*(8*j-3))) * (1-x^(i*(8*j-5))) / ((1-x^(i*(8*j-1))) * (1-x^(i*(8*j-7)))).
%F A327851 G.f.: Product_{k>=1} (1-x^k)^(-A035185(k)).
%t A327851 nmax = 60; CoefficientList[Series[Product[QPochhammer[x^(8*j - 3)] * QPochhammer[x^(8*j - 5)]/(QPochhammer[x^(8*j - 7)] * QPochhammer[x^(8*j - 1)]), {j, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 28 2019 *)
%o A327851 (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^k)^sumdiv(k, d, kronecker(2, d))))
%Y A327851 Convolution inverse of A327852.
%Y A327851 Product_{k>=1} (1 - x^k)^(- Sum_{d|k} (b/d)), where (m/n) is the Kronecker symbol: this sequence (b=2), A107742 (b=4), A327716 (b=5).
%Y A327851 Cf. A035185, A111374.
%K A327851 nonn
%O A327851 0,3
%A A327851 _Seiichi Manyama_, Sep 28 2019