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 A337026 #15 Dec 25 2023 10:02:22
%S A337026 1,2,7,38,277,2522,27547,351038,5112457,83764082,1524907087,
%T A337026 30536665238,667096092637,15787642820042,402374890155427,
%U A337026 10987722264846638,320046586135452817,9904844539648850402,324568009210656076567,11226512280285374623238
%N A337026 a(n) = (2/3) * Sum_{k>=0} (2*k + 1)^n / 3^k.
%H A337026 G. C. Greubel, <a href="/A337026/b337026.txt">Table of n, a(n) for n = 0..400</a>
%F A337026 E.g.f.: 2 * exp(x) / (3 - exp(2*x)).
%F A337026 a(n) = Sum_{k=0..n} binomial(n,k) * A122704(k).
%F A337026 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A123227(k).
%F A337026 a(n) ~ n! * 2^(n+1) / (sqrt(3) * log(3)^(n+1)). - _Vaclav Kotesovec_, Mar 27 2022
%F A337026 a(n) = 1 + Sum_{k=1..n} 2^(k-1) * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Dec 24 2023
%t A337026 Table[2^(n + 1) HurwitzLerchPhi[1/3, -n, 1/2]/3, {n, 0, 19}]
%t A337026 nmax = 19; CoefficientList[Series[2 Exp[x]/(3 - Exp[2 x]), {x, 0, nmax}], x] Range[0, nmax]!
%o A337026 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( 2*Exp(x)/(3-Exp(2*x)) ))); // _G. C. Greubel_, Jun 09 2022
%o A337026 (Sage)
%o A337026 def A337026_list(prec):
%o A337026 P.<x> = PowerSeriesRing(QQ, prec)
%o A337026 return P( 2*exp(x)/(3-exp(2*x)) ).egf_to_ogf().list()
%o A337026 A337026_list(40) # _G. C. Greubel_, Jun 09 2022
%Y A337026 Cf. A080253, A122704, A123227.
%K A337026 nonn
%O A337026 0,2
%A A337026 _Ilya Gutkovskiy_, Aug 11 2020