A376351 - OEIS

%I #12 Sep 21 2024 13:25:46

%S 1,0,0,6,0,60,2520,840,181440,6063120,11642400,1437337440,44626982400,

%T 254278664640,24575197046400,756010400745600,9284429893939200,

%U 784770965801222400,25067890370095372800,541810656586725926400,42351473267452597248000,1461224653966598493772800,48020130717168717960652800

%N E.g.f. satisfies A(x) = exp( x*A(x)*(exp(x^2*A(x)^2) - 1) ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F E.g.f.: (1/x) * Series_Reversion( x*exp(x*(1 - exp(x^2))) ).

%F a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-2*k-1) * Stirling2(k,n-2*k)/k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(x*(1-exp(x^2))))/x))

%o (PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*stirling(k, n-2*k, 2)/k!);

%Y Cf. A030019, A356785, A371145.

%Y Cf. A357966.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 21 2024