A380800 Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-x / (1 - x)^2) * (1 - x)^3 ) )^2.

1, 8, 142, 4088, 165576, 8711752, 566093104, 43882188408, 3957135262720, 407285038758536, 47138933615042304, 6062383519783848952, 857919091977394542592, 132511278843714141837000, 22185703881021997753194496, 4002648943012304165391154808, 774212130931445685605345918976

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)^(1/2) / (1 - x*A(x)^(1/2))^2 ) / (1 - x*A(x)^(1/2))^6.

a(n) = 2 * n! * Sum_{k=0..n} (n+2)^(k-1) * binomial(4*n+k+5,n-k)/k!.

Prog

(PARI) a(n, q=2, r=1, s=1, t=2, u=3) = 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!);

Crossrefs

Cf. A380799, A380801.

Sequence in context: A295242 A305763 A180357 * A373874 A317112 A320396

Adjacent sequences: A380797 A380798 A380799 * A380801 A380802 A380803

Keyword

nonn

Author

Seiichi Manyama, Feb 04 2025

Status

approved