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 A378043 #11 Feb 16 2025 08:34:07
%S A378043 1,2,13,190,4045,116746,4251289,187255174,9684799961,575477786674,
%T A378043 38638577549701,2893159369162030,239045577899472997,
%U A378043 21604942464613062010,2120362938300115706513,224568728344893756230326,25529660577970226603535793,3100816199696659908092912866
%N A378043 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).
%H A378043 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378043 E.g.f.: (1+x) * exp( -LambertW(-2*x*(1+x)^3)/2 ).
%F A378043 a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(3*k+1,n-k)/k!.
%o A378043 (PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(3*k+1, n-k)/k!);
%Y A378043 Cf. A378019, A378044.
%Y A378043 Cf. A377894, A378045.
%Y A378043 Cf. A377894.
%K A378043 nonn
%O A378043 0,2
%A A378043 _Seiichi Manyama_, Nov 15 2024