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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327716 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A003823.

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%I A327716 #27 Feb 16 2025 08:33:58
%S A327716 1,1,1,1,2,3,3,3,4,6,7,9,10,12,14,17,21,23,26,32,40,45,51,58,69,80,89,
%T A327716 102,116,135,154,177,198,224,253,288,326,361,408,459,521,583,650,723,
%U A327716 812,909,1009,1122,1244,1393,1547,1716,1898,2101,2326,2575,2845,3132,3456,3809
%N A327716 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A003823.
%C A327716 a(n) > 0.
%H A327716 Vaclav Kotesovec, <a href="/A327716/b327716.txt">Table of n, a(n) for n = 0..10000</a>
%H A327716 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction.</a>
%F A327716 G.f.: Product_{i>=1} Product_{j>=1} (1-x^(i*(5*j-2))) * (1-x^(i*(5*j-3))) / ((1-x^(i*(5*j-1))) * (1-x^(i*(5*j-4)))).
%F A327716 G.f.: Product_{k>=1} (1-x^k)^(-A035187(k)).
%F A327716 a(n) ~ c * exp(Pi*sqrt(r*n)) / n^(3/4), where r = 4*log((1+sqrt(5))/2) / (3*sqrt(5)) = 0.2869392939760026925..., c = 0.203427046022096... - _Vaclav Kotesovec_, Sep 24 2019, updated May 09 2020
%t A327716 nmax = 60; CoefficientList[Series[Product[QPochhammer[x^(5*j - 3)] * QPochhammer[x^(5*j - 2)]/(QPochhammer[x^(5*j - 4)] * QPochhammer[x^(5*j - 1)]), {j, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 23 2019 *)
%o A327716 (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^k)^sumdiv(k, d, kronecker(5, d))))
%Y A327716 Convolution inverse of A327688.
%Y A327716 Cf. A003823, A035187, A327690, A327691, A327694, A327717, A327718, A327719, A327720.
%K A327716 nonn
%O A327716 0,5
%A A327716 _Seiichi Manyama_, Sep 23 2019