A379937 - OEIS

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

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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)!);