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 A376389 #15 Sep 22 2024 11:28:12
%S A376389 1,2,16,236,5172,151452,5568452,246816236,12817081828,763506280700,
%T A376389 51333645252228,3845783934171852,317719919221661540,
%U A376389 28697779828343464412,2813593953407672094724,297587218343306095847084,33775895041558685181041892,4094844200848292606224524732
%N A376389 Expansion of e.g.f. (1/x) * Series_Reversion( x*(2 - exp(x))^2 ).
%H A376389 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A376389 E.g.f. A(x) satisfies A(x) = 1/(2 - exp(x*A(x)))^2.
%F A376389 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367134.
%F A376389 a(n) = (2/(2*n+2)!) * Sum_{k=0..n} (2*n+k+1)! * Stirling2(n,k).
%F A376389 a(n) ~ 2^n * LambertW(exp(1/2))^(2*n + 2)*n^(n-1) / (sqrt(1 + LambertW(exp(1/2))) * exp(n) * (2*LambertW(exp(1/2)) - 1)^(3*n + 2)). - _Vaclav Kotesovec_, Sep 22 2024
%o A376389 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(2-exp(x))^2)/x))
%o A376389 (PARI) a(n) = 2*sum(k=0, n, (2*n+k+1)!*stirling(n, k, 2))/(2*n+2)!;
%Y A376389 Cf. A005649, A367134.
%K A376389 nonn
%O A376389 0,2
%A A376389 _Seiichi Manyama_, Sep 22 2024