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 A378016 #8 Feb 16 2025 08:34:07
%S A378016 1,2,11,115,1617,30241,701923,19517975,633387905,23513238865,
%T A378016 983268873891,45750603668815,2344878934878769,131285573039583977,
%U A378016 7973124098907905603,522086636316439329511,36669284618683152764289,2750044026126526125774625,219342360538110975815216323
%N A378016 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x)^2 * A(x) ).
%H A378016 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378016 E.g.f.: (1+x) * exp( -LambertW(-x * (1+x)^3) ).
%F A378016 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(3*k+1,n-k)/k!.
%o A378016 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)*exp(-lambertw(-x*(1+x)^3))))
%o A378016 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+1, n-k)/k!);
%Y A378016 Cf. A376145, A377828, A378017.
%Y A378016 Cf. A377964.
%K A378016 nonn
%O A378016 0,2
%A A378016 _Seiichi Manyama_, Nov 14 2024