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.
%I A271236 #27 Feb 28 2024 18:10:15
%S A271236 1,3,45,450,5805,52326,705591,6190425,77219325,751178610,8522919063,
%T A271236 80502824835,975122402985,8949951461925,100088881882830,
%U A271236 1003346683458480,10828622925516312,104307212166072165,1152197107898173875,11048535008792967825,119509353627934830327
%N A271236 G.f.: Product_{k>=1} 1/(1 - (9*x)^k)^(1/3).
%C A271236 In general, for h>=1, if g.f. = Product_{k>=1} 1/(1-(h^2*x)^k)^(1/h), then a(n) ~ h^(2*n) * exp(Pi*sqrt(2*n/(3*h))) / (2^(5*h+3) * 3^(h+1) * h^(h+1) * n^(3*h+1))^(1/(4*h)).
%C A271236 This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/3, g(n) = 9^n. - _Seiichi Manyama_, Apr 20 2018
%H A271236 Vaclav Kotesovec, <a href="/A271236/b271236.txt">Table of n, a(n) for n = 0..1000</a>
%F A271236 a(n) ~ 3^(2*n - 2/3) * exp(sqrt(2*n)*Pi/3) / (2^(3/2) * n^(5/6)).
%t A271236 nmax = 30; CoefficientList[Series[Product[1/(1 - (9*x)^k)^(1/3), {k, 1, nmax}], {x, 0, nmax}], x]
%o A271236 (PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, 1/(1-(9*x)^k)^(1/3))) \\ _Altug Alkan_, Apr 20 2018
%Y A271236 Cf. A298994, A303074, A303130, A303152, A303342, A370735.
%Y A271236 Expansion of Product_{n>=1} (1 - ((b^2)*x)^n)^(-1/b): A000041 (b=1), A271235 (b=2), this sequence (b=3), A303135 (b=4), A303136 (b=5).
%K A271236 nonn
%O A271236 0,2
%A A271236 _Vaclav Kotesovec_, Apr 02 2016