A379937 E.g.f. A(x) satisfies A(x) = ( exp(-x*A(x)^(1/2)) + x*A(x) )^2.

1, 0, 2, 4, 48, 328, 4240, 52092, 842240, 14598352, 294741504, 6501719860, 159434125312, 4248764847000, 123112522876928, 3840463241458732, 128576024097914880, 4594095412384753312, 174592522399006720000, 7030376888543624506212, 299062278252922180468736

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1-x)*exp(x))/x)^2))
(PARI) a(n) = -2*n!*sum(k=0, n, (-n-2)^(n-k-1)*binomial(n+k+1, k)/(n-k)!);

Crossrefs

Cf. A379866, A379932.

Cf. A377859.

Sequence in context: A212429 A298903 A127211 * A144580 A144578 A143968

Adjacent sequences: A379934 A379935 A379936 * A379938 A379939 A379940

Keyword

nonn,new

Author

Seiichi Manyama, Jan 06 2025

Status

approved