A380945 - OEIS

A380945

Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-2*x) ).

1, 4, 50, 1124, 37192, 1637232, 90278176, 5992556320, 465599728512, 41470892979200, 4167168740195584, 466428111222196224, 57556315795242096640, 7763511917730857967616, 1136484206117494859980800, 179453678311835212416585728, 30404317385796994658988752896

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

Index entries for reversions of series

FORMULA

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380723.

a(n) = 2 * n! * Sum_{k=0..n} (2*n+2)^(k-1) * binomial(3*n-k+1,n-k)/k!.

PROG

(PARI) a(n, q=2, r=2, s=2, t=0, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);