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 A371009 #16 Nov 07 2024 15:42:08
%S A371009 1,-1,0,8,-16,-336,2464,30176,-572160,-3654400,193852928,-29664768,
%T A371009 -88869165056,788014352384,51013392617472,-1125131950034944,
%U A371009 -33201578814668800,1536045242886979584,19518336239699623936,-2267097378027280924672
%N A371009 Expansion of e.g.f. (1/x) * Series_Reversion( 2*x/(3 - exp(2*x)) ).
%H A371009 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371009 a(n) = 1/(2*(n+1)) * Sum_{k=0..n+1} (-1)^k * 3^(n+1-k) * k^n * binomial(n+1,k).
%F A371009 a(n) = n! * Sum_{k=0..n} (-1)^k * 2^(n-k) * Stirling2(n,k)/(n-k+1)!. - _Seiichi Manyama_, Nov 07 2024
%o A371009 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(2*x/(3-exp(2*x)))/x))
%o A371009 (PARI) a(n) = sum(k=0, n+1, (-1)^k*3^(n+1-k)*k^n*binomial(n+1, k))/(2*(n+1));
%Y A371009 Cf. A371007, A371008.
%K A371009 sign
%O A371009 0,4
%A A371009 _Seiichi Manyama_, Mar 08 2024