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 A362735 #19 Feb 16 2025 08:34:05
%S A362735 1,2,-4,56,-1008,25632,-833600,33067904,-1548418816,83597525504,
%T A362735 -5112566055936,349330707068928,-26374805535322112,
%U A362735 2180554321981349888,-195926186031705505792,19010400989418574020608,-1980997069982960384409600,220651645970702249702326272
%N A362735 E.g.f. satisfies A(x) = exp(x + x / A(x)^2).
%H A362735 Seiichi Manyama, <a href="/A362735/b362735.txt">Table of n, a(n) for n = 0..339</a>
%H A362735 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362735 E.g.f.: sqrt( 2*x / LambertW(2*x*exp(-2*x)) ) = exp( x + LambertW(2*x*exp(-2*x))/2 ).
%F A362735 a(n) = Sum_{k=0..n} (-2*k+1)^(n-1) * binomial(n,k) = 2^n * A349720(n).
%o A362735 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(2*x*exp(-2*x))/2)))
%Y A362735 Cf. A349562, A362693, A362694, A362734.
%Y A362735 Cf. A349720.
%K A362735 sign
%O A362735 0,2
%A A362735 _Seiichi Manyama_, May 01 2023