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 A261330 #12 Feb 16 2025 08:33:26
%S A261330 1,2,9,30,106,348,1153,3698,11798,37034,115294,355202,1086080,3294912,
%T A261330 9931019,29745296,88597104,262508288,774073787,2272321666,6642701371,
%U A261330 19342768210,56117550874,162247236638,467563212923,1343273262184,3847866714452,10991864363660
%N A261330 Euler transform of Pell-Lucas numbers.
%H A261330 Vaclav Kotesovec, <a href="/A261330/b261330.txt">Table of n, a(n) for n = 0..1000</a>
%H A261330 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1508.01796">Asymptotics of the Euler transform of Fibonacci numbers</a>, arXiv:1508.01796 [math.CO], Aug 07 2015
%H A261330 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellNumber.html">Pell Number</a>
%H A261330 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pell_number">Pell number</a>
%F A261330 G.f.: Product_{k>=1} 1/(1-x^k)^(A002203(k)).
%F A261330 a(n) ~ (1+sqrt(2))^n * exp(-1 + 2^(-3/2) + 2*sqrt(n) + s) / (2 * sqrt(Pi) * n^(3/4)), where s = Sum_{k>=2} = 2/(((1+sqrt(2))^k + 2/(1 + (1+sqrt(2))^k) - 3)*k) = 0.40371233206538058741995064489690066306587648488344483...
%t A261330 nmax=40; cPell[0]=2; cPell[1]=2; cPell[n_]:=cPell[n] = 2*cPell[n-1] + cPell[n-2]; CoefficientList[Series[Product[1/(1-x^k)^cPell[k], {k, 1, nmax}], {x, 0, nmax}], x]
%Y A261330 Cf. A002203, A261329, A261331, A261332, A166861, A261031.
%K A261330 nonn
%O A261330 0,2
%A A261330 _Vaclav Kotesovec_, Aug 15 2015