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 A261329 #18 Feb 16 2025 08:33:26
%S A261329 1,1,3,8,23,62,175,477,1319,3602,9851,26779,72726,196724,531157,
%T A261329 1430144,3842911,10303055,27570786,73637306,196333303,522584286,
%U A261329 1388786089,3685169795,9764703347,25838430572,68282175170,180221449469,475102410065,1251038486529
%N A261329 Euler transform of Pell numbers.
%H A261329 Vaclav Kotesovec, <a href="/A261329/b261329.txt">Table of n, a(n) for n = 0..1000</a>
%H A261329 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 A261329 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellNumber.html">Pell Number</a>
%H A261329 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pell_number">Pell number</a>
%F A261329 G.f.: Product_{k>=1} 1/(1-x^k)^(A000129(k)).
%F A261329 a(n) ~ (1+sqrt(2))^n * exp(-1/8 + 2^(1/4)*sqrt(n) + s) / (2^(11/8) * sqrt(Pi) * n^(3/4)), where s = Sum_{k>=2} 1/(((sqrt(2)+1)^k - (sqrt(2)-1)^k - 2)*k) = 0.17615706029370539578355193664752741450665073523628663099586621933373...
%F A261329 G.f.: exp(Sum_{k>=1} x^k/(k*(1 - 2*x^k - x^(2*k)))). - _Ilya Gutkovskiy_, May 30 2018
%t A261329 nmax=40; Pell[0]=0; Pell[1]=1; Pell[n_]:=Pell[n] = 2*Pell[n-1] + Pell[n-2]; CoefficientList[Series[Product[1/(1-x^k)^Pell[k], {k, 1, nmax}], {x, 0, nmax}], x]
%o A261329 (SageMath) # uses[EulerTransform from A166861]
%o A261329 a = BinaryRecurrenceSequence(2, 1)
%o A261329 b = EulerTransform(a)
%o A261329 print([b(n) for n in range(30)]) # _Peter Luschny_, Nov 11 2020
%Y A261329 Cf. A000129, A261330, A261331, A261332, A166861, A261031.
%K A261329 nonn
%O A261329 0,3
%A A261329 _Vaclav Kotesovec_, Aug 15 2015