cp's OEIS Frontend

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.

A370750 a(n) = 9^n * [x^n] Product_{k>=1} ((1 + 2*x^k)/(1 - 2*x^k))^(1/3).

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%I A370750 #6 Feb 29 2024 10:47:38
%S A370750 1,12,180,3852,50436,947052,14087844,245858652,3531115620,64019229660,
%T A370750 950199749748,16959724619004,256888616329044,4642974930688812,
%U A370750 71716402072904724,1308491345357401068,20501966472318764388,376230182366985289164,5987314157007778195716,110286515004790197907836
%N A370750 a(n) = 9^n * [x^n] Product_{k>=1} ((1 + 2*x^k)/(1 - 2*x^k))^(1/3).
%F A370750 G.f.: Product_{k>=1} ((1 + 2*(9*x)^k)/(1 - 2*(9*x)^k))^(1/3).
%F A370750 a(n) ~ QPochhammer(-1, 1/2)^(1/3) * 18^n / (Gamma(1/3) * QPochhammer(1/2)^(1/3) * n^(2/3)).
%t A370750 nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k)/(1 - 2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]
%t A370750 nmax = 20; CoefficientList[Series[Product[(1 + 2*(9*x)^k)/(1 - 2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]
%Y A370750 Cf. A261584, A303346, A370749.
%Y A370750 Cf. A032302, A070933.
%Y A370750 Cf. A370716, A370715.
%K A370750 nonn
%O A370750 0,2
%A A370750 _Vaclav Kotesovec_, Feb 29 2024