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 A376350 #8 Sep 21 2024 13:25:36 %S A376350 1,0,0,6,0,60,2520,1680,181440,6138720,18295200,1444988160, %T A376350 46443196800,357015859200,25016537145600,818965321574400, %U A376350 12259854032025600,815066633667686400,28461465853402982400,691667282863484928000,45198900807076912896000,1739192274792359202816000,60318174486002275287244800 %N A376350 E.g.f. satisfies A(x) = 1/(1 - x^2*A(x)^2)^(x*A(x)). %H A376350 <a href="/index/Res#revert">Index entries for reversions of series</a> %F A376350 E.g.f.: (1/x) * Series_Reversion( x*(1 - x^2)^x ). %F A376350 a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-2*k-1) * |Stirling1(k,n-2*k)|/k!. %o A376350 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2)^x)/x)) %o A376350 (PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*abs(stirling(k, n-2*k, 1))/k!); %Y A376350 Cf. A001761, A184949, A371147. %Y A376350 Cf. A353226. %K A376350 nonn %O A376350 0,4 %A A376350 _Seiichi Manyama_, Sep 21 2024