A389444 - OEIS

A389444

Expansion of (1/x) * Series_Reversion( x * (1 / (1 + x) - x^4) ).

1, 1, 1, 1, 2, 8, 29, 85, 216, 529, 1393, 4083, 12594, 38446, 113953, 332300, 975253, 2918838, 8886236, 27234516, 83375623, 254664534, 778530177, 2389985106, 7374537938, 22842820639, 70903108970, 220323430866, 685430468527, 2135987798170, 6669803026849, 20867531095280

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

OFFSET

0,5

LINKS

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

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(n+k+1,n-4*k).

a(n) = (1/(n+1)) * [x^n] 1/(1 / (1 + x) - x^4)^(n+1).

MATHEMATICA

Table[SeriesCoefficient[1/(1/(1+x)-x^4)^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 17 2025 *)

PROG

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x)-x^4))/x)