%I #12 Sep 02 2024 08:38:25
%S 1,-2,4,-2,-52,358,12,-25986,247228,821398,-52933300,534428926,
%T 6201248220,-271179578490,2375560802188,75726973445374,
%U -2740636867741828,14280527041851958,1501820173046702796,-46939564687781824002,-67963035486950641508
%N E.g.f. satisfies A(x) = (2 - exp(x * A(x)^(1/2)))^2.
%F E.g.f.: A(x) = ( (1/x) * Series_Reversion(x / (2 - exp(x))) )^2.
%F a(n) = 2 * (n+1)! * Sum_{k=0..n} (-1)^k * Stirling2(n,k)/(n-k+2)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((serreverse(x/(2-exp(x)))/x)^2))
%o (PARI) a(n) = 2*(n+1)!*sum(k=0, n, (-1)^k*stirling(n, k, 2)/(n-k+2)!);
%Y Cf. A007334, A097718, A375897.
%K sign
%O 0,2
%A _Seiichi Manyama_, Sep 02 2024