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 A377546 #10 Nov 01 2024 09:32:59
%S A377546 1,2,18,294,7136,231410,9421932,462459242,26593896912,1754278123266,
%T A377546 130611457831700,10835721949072922,991315043401627320,
%U A377546 99154012317212577218,10765112531819005907484,1260860266373297376720810,158473050112495481401395872,21275613503385328981848681986
%N A377546 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x))^2 ).
%H A377546 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A377546 E.g.f. satisfies A(x) = 1/(1 - x * A(x) * exp(x*A(x)))^2.
%F A377546 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364985.
%F A377546 a(n) = 2 * n! * Sum_{k=0..n} k^(n-k) * binomial(2*n+k+2,k)/( (2*n+k+2)*(n-k)! ).
%o A377546 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x))^2)/x))
%o A377546 (PARI) a(n) = 2*n!*sum(k=0, n, k^(n-k)*binomial(2*n+k+2, k)/((2*n+k+2)*(n-k)!));
%Y A377546 Cf. A213644, A377548.
%Y A377546 Cf. A364985.
%K A377546 nonn
%O A377546 0,2
%A A377546 _Seiichi Manyama_, Oct 31 2024