A379937 - OEIS

%I #11 Jan 07 2025 07:00:28

%S 1,0,2,4,48,328,4240,52092,842240,14598352,294741504,6501719860,

%T 159434125312,4248764847000,123112522876928,3840463241458732,

%U 128576024097914880,4594095412384753312,174592522399006720000,7030376888543624506212,299062278252922180468736

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

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377859.

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

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

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

%Y Cf. A379866, A379932.

%Y Cf. A377859.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 06 2025