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 A308418 #18 May 30 2019 03:59:19
%S A308418 1,1,7,73,649,8821,122311,2064637,37933393,773276329,17257075111,
%T A308418 414876953041,10780187135257,298418920103773,8812636845668839,
%U A308418 275368711393020421,9091457478119636641,315782978460465185617,11511089733834178827463,439231563093877354663129
%N A308418 Expansion of e.g.f. exp(x*(1 + 3*x + 6*x^2 + 3*x^3 + x^4)/(1 - x^2)^3).
%F A308418 E.g.f.: exp(Sum_{k>=1} J_2(k)*x^k/(1 - x^(2*k))), where J_2() is the Jordan function (A007434).
%F A308418 E.g.f.: Product_{k>=1} (1 + x^k)^(J_3(k)/k), where J_3() is the Jordan function (A059376).
%F A308418 a(n) ~ 2^(-5/4) * 21^(1/8) * n^(n - 1/8) * exp(2^(3/2) * 3^(-3/4) * 7^(1/4) * n^(3/4) - n). - _Vaclav Kotesovec_, May 28 2019
%F A308418 E.g.f.: exp(Sum_{k>=1} A308422(k)*x^k). - _Ilya Gutkovskiy_, May 29 2019
%t A308418 nmax = 19; CoefficientList[Series[Exp[x (1 + 3 x + 6 x^2 + 3 x^3 + x^4)/(1 - x^2)^3], {x, 0, nmax}], x] Range[0, nmax]!
%t A308418 nmax = 19; CoefficientList[Series[Product[(1 + x^k)^(DirichletConvolve[j^3, MoebiusMu[j], j, k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A308418 a[n_] := a[n] = Sum[1/8 (7 - (-1)^k) k^2 k! Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]
%o A308418 (PARI) my(x ='x + O('x^30)); Vec(serlaplace(exp(x*(1+3*x+6*x^2+3*x^3+x^4)/(1-x^2)^3))) \\ _Michel Marcus_, May 26 2019
%Y A308418 Cf. A007434, A059376, A088009, A255807, A308417, A308422.
%K A308418 nonn
%O A308418 0,3
%A A308418 _Ilya Gutkovskiy_, May 25 2019