A389658 - OEIS

A389658

Expansion of (1/x) * Series_Reversion( x / (1 + x^2 / (1 - x)^2)^2 ).

1, 0, 2, 4, 15, 52, 192, 732, 2853, 11340, 45756, 186964, 772057, 3216912, 13507936, 57103516, 242831553, 1038056904, 4458248878, 19227639168, 83239247342, 361591141112, 1575659134512, 6885666506004, 30169456622015, 132506539685052, 583278733961600, 2572843291435872

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

OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

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

a(n) = (1/(n+1)) * [x^n] (1 + x^2 / (1 - x)^2)^(2*(n+1)).

MATHEMATICA

Table[SeriesCoefficient[(1+x^2/(1-x)^2)^(2*(n+1)), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 20 2025 *)

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x^2/(1-x)^2)^2)/x)