A380778 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x / (1 + x)^2) / (1 + x)^2 ).

1, 3, 21, 238, 3777, 77616, 1966381, 59379888, 2085295617, 83580555520, 3767468068581, 188731359078912, 10405256927541889, 626236791181897728, 40860738460515664125, 2873352871221375440896, 216652727562188159522049, 17437704874236857627246592, 1492289181734461545084103477

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for reversions of series

Formula

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

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

Prog

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

Crossrefs

Cf. A377829, A380779, A380780, A380781.

Cf. A380674.

Sequence in context: A302703 A334262 A375900 * A234855 A367375 A058562

Adjacent sequences: A380775 A380776 A380777 * A380779 A380780 A380781

Keyword

nonn,new

Author

Seiichi Manyama, Feb 02 2025

Status

approved