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 A365056 #18 Feb 16 2025 08:34:06
%S A365056 1,1,0,1,-6,46,-440,5076,-68740,1070056,-18835164,369994780,
%T A365056 -8025080096,190501729848,-4912802070280,136775150153656,
%U A365056 -4088669684755440,130620500241909376,-4441243727496127184,160132524268963159440,-6102784264210449418144
%N A365056 E.g.f. satisfies A(x) = exp( x * (1+x/2)/A(x) ).
%H A365056 Seiichi Manyama, <a href="/A365056/b365056.txt">Table of n, a(n) for n = 0..403</a>
%H A365056 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A365056 E.g.f.: exp( LambertW(x * (1+x/2)) ).
%F A365056 a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (-k+1)^(k-1) * binomial(k,n-k)/k!.
%o A365056 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x*(1+x/2)))))
%Y A365056 Cf. A365053, A365054, A365055.
%Y A365056 Cf. A365038.
%K A365056 sign
%O A365056 0,5
%A A365056 _Seiichi Manyama_, Aug 19 2023