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 A360609 #39 Feb 16 2025 08:34:04
%S A360609 1,2,17,313,9053,357941,17975605,1095604133,78570635225,6482415935449,
%T A360609 604889610870881,62989604872166897,7241672622495518773,
%U A360609 911048848278644776949,124497704904842673086285,18364053909500922198147421,2908158473059042016441887025
%N A360609 E.g.f. satisfies A(x) = exp(x*A(x)^3) / (1-x).
%H A360609 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A360609 E.g.f.: (LambertW( -3*x/(1-x)^3 ) / (-3*x))^(1/3).
%F A360609 a(n) ~ 3^(-5/6) * (2^(4/3) + 2*(3 + sqrt(4*exp(1) + 9))^(1/3) * exp(-2/3) - 2^(2/3) * (3 + sqrt(4*exp(1) + 9))^(2/3) * exp(-1/3))^(1/6) * 2^(1/3) * (3 + sqrt(4*exp(1) + 9))^(4/9) * sqrt(4 - 2^(4/3) * (3 + sqrt(4*exp(1) + 9))^(2/3) * exp(-1/3) + 3*2^(2/3) * exp(-2/3) * (3 + sqrt(4*exp(1) + 9))^(1/3)) * n^(n-1) * (12 + 4*sqrt(4*exp(1) + 9))^(n/3) / (exp(7/18 + 5*n/3) * (2 - 2^(1/3) * (3 + sqrt(4*exp(1) + 9))^(2/3) * exp(-1/3) + exp(-2/3) * (12 + 4*sqrt(4*exp(1) + 9))^(1/3))^n * ((3 + sqrt(4*exp(1) + 9))^(2/3) * exp(-1/3) - 2^(2/3))^(3/2) * sqrt(2^(1/3) * (3 + sqrt(4*exp(1) + 9))^(2/3) * exp(-1/3) - 2)). - _Vaclav Kotesovec_, Mar 06 2023
%F A360609 a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(n+2*k,n-k)/k!. - _Seiichi Manyama_, Mar 09 2024
%o A360609 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(-3*x/(1-x)^3)/(-3*x))^(1/3)))
%Y A360609 Cf. A352410, A360601.
%Y A360609 Cf. A052752, A361182.
%Y A360609 Cf. A370876.
%K A360609 nonn
%O A360609 0,2
%A A360609 _Seiichi Manyama_, Mar 05 2023