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 A308417 #11 May 29 2019 04:12:14
%S A308417 1,1,3,25,145,1461,14011,169933,2231265,32572585,528302611,9146070561,
%T A308417 174016032433,3498446485405,75954922790475,1737982233878101,
%U A308417 42327522277348801,1084073452000879953,29253450397798616995,827617575903336189865,24503022168956714812881
%N A308417 Expansion of e.g.f. exp(x*(1 + x + x^2)/(1 - x^2)^2).
%F A308417 E.g.f.: exp(Sum_{k>=1} A026741(k)*x^k).
%F A308417 E.g.f.: Product_{k>=1} (1 + x^k)^(J_2(k)/k), where J_2() is the Jordan function (A007434).
%F A308417 a(0) = 1; a(n) = Sum_{k=1..n} A026741(k)*k!*binomial(n-1,k-1)*a(n-k).
%F A308417 a(n) ~ 2^(-1/6) * 3^(-1/3) * n^(n - 1/6) * exp((3/2)^(4/3) * n^(2/3) - n). - _Vaclav Kotesovec_, May 29 2019
%t A308417 nmax = 20; CoefficientList[Series[Exp[x (1 + x + x^2)/(1 - x^2)^2], {x, 0, nmax}], x] Range[0, nmax]!
%t A308417 nmax = 20; CoefficientList[Series[Product[(1 + x^k)^(DirichletConvolve[j^2, MoebiusMu[j], j, k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A308417 a[n_] := a[n] = Sum[Numerator[k/2] k! Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 20}]
%o A308417 (PARI) my(x ='x + O('x^30)); Vec(serlaplace(exp(x*(1 + x + x^2)/(1 - x^2)^2))) \\ _Michel Marcus_, May 26 2019
%Y A308417 Cf. A007434, A026741, A082579, A088009, A301876, A308418.
%K A308417 nonn
%O A308417 0,3
%A A308417 _Ilya Gutkovskiy_, May 25 2019