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 A362654 #19 Aug 05 2025 09:03:14
%S A362654 1,1,3,22,197,2316,33967,595624,12190761,285479056,7531645211,
%T A362654 221124649824,7152276636397,252742471065280,9688895208298503,
%U A362654 400510408002257536,17759663471017945553,840937887639033467136,42351198256293556043827
%N A362654 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x) ).
%H A362654 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362654 E.g.f.: exp( -LambertW(-x * exp(x^2)) ).
%F A362654 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (n-2*k+1)^(n-2*k-1) / (k! * (n-2*k)!).
%F A362654 a(n) ~ sqrt(1 + LambertW(2*exp(-2))) * 2^(n/2) * n^(n-1) / (exp(n-1) * LambertW(2*exp(-2))^(n/2)). - _Vaclav Kotesovec_, Aug 05 2025
%o A362654 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*exp(x^2)))))
%Y A362654 Cf. A273954, A362655.
%Y A362654 Cf. A362653, A362673.
%K A362654 nonn
%O A362654 0,3
%A A362654 _Seiichi Manyama_, Apr 28 2023