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 A261565 #17 Jun 06 2024 12:25:19
%S A261565 1,3,15,54,201,672,2268,7266,23208,72414,224652,688929,2103975,
%T A261565 6386907,19337091,58367817,175905741,529331190,1591515297,4781575074,
%U A261565 14359673454,43108645230,129387584991,388283978589,1165099808574,3495782937135,10488322595625
%N A261565 Expansion of Product_{k>=1} (1/(1 - 3*x^k))^k.
%C A261565 In general, for z > 1 or z < -1, if g.f. = Product_{k>=1} (1/(1 - z*x^k))^k, then a(n) ~ c * z^n, where c = Product_{j>=1} 1/(1 - 1/z^j)^(j+1).
%H A261565 Vaclav Kotesovec, <a href="/A261565/b261565.txt">Table of n, a(n) for n = 0..1000</a>
%F A261565 a(n) ~ c * 3^n, where c = Product_{j>=1} 1/(1 - 1/3^j)^(j+1) = 4.1269357592430271005054028580646705856298720432004233223482475759761040273...
%F A261565 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} 3^d * n^2/d^2 ). - _Paul D. Hanna_, Sep 30 2015
%t A261565 nmax = 40; CoefficientList[Series[Product[(1/(1 - 3*x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t A261565 nmax = 40; CoefficientList[Series[Exp[Sum[3^k/k*x^k/(1 - x^k)^2, {k, 1, nmax}]], {x, 0, nmax}], x]
%o A261565 (PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, 3^d * m^2/d^2) ) +x*O(x^n)), n)}
%o A261565 for(n=0, 40, print1(a(n), ", ")) \\ _Paul D. Hanna_, Sep 30 2015
%Y A261565 Cf. A000219, A242587, A246935, A261561.
%K A261565 nonn
%O A261565 0,2
%A A261565 _Vaclav Kotesovec_, Aug 24 2015