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 A362492 #15 Feb 16 2025 08:34:05
%S A362492 1,1,0,-8,-38,106,3676,24508,-296036,-9149156,-56500064,2211573376,
%T A362492 64958496472,184823374360,-35372361487280,-971135892546224,
%U A362492 4364710018963216,1034808592156017424,25290798052846014208,-474242641154857953152,-49625273567646267051104
%N A362492 E.g.f. satisfies A(x) = exp(x - x^2/2 * A(x)^2).
%H A362492 Robert Israel, <a href="/A362492/b362492.txt">Table of n, a(n) for n = 0..403</a>
%H A362492 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362492 E.g.f.: exp(x - LambertW(x^2 * exp(2*x))/2) = sqrt( LambertW(x^2 * exp(2*x))/x^2 ).
%F A362492 a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * (2*k+1)^(n-k-1) / (k! * (n-2*k)!).
%p A362492 N:= 50: # for a(0)..a(N)
%p A362492 egf:= exp(x - LambertW(x^2 * exp(2*x))/2):
%p A362492 S:=series(egf,x,N+1):
%p A362492 [seq](coeff(S,x,i)*i!,i=0..N); # _Robert Israel_, May 22 2023
%o A362492 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2*exp(2*x))/2)))
%Y A362492 Cf. A362493, A362494.
%Y A362492 Cf. A362480.
%K A362492 sign
%O A362492 0,4
%A A362492 _Seiichi Manyama_, Apr 22 2023