A389350 - OEIS

A389350

Expansion of (1/x) * Series_Reversion( x * (1 - x^3 / (1 - x)^4) ).

1, 0, 0, 1, 4, 10, 24, 71, 236, 766, 2412, 7679, 25112, 83346, 277604, 927516, 3118160, 10552178, 35887960, 122513583, 419694656, 1442734382, 4975498904, 17207820546, 59666413296, 207380778872, 722394566160, 2521613633971, 8818892177476, 30897476078130, 108431536363628

(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/3)} binomial(n+k,k) * binomial(n+k-1,n-3*k).

a(n) = (1/(n+1)) * [x^n] 1/(1 - x^3 / (1 - x)^4)^(n+1).

MATHEMATICA

Table[SeriesCoefficient[1/(1-x^3/(1-x)^4)^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 18 2025 *)

PROG

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x^3/(1-x)^4))/x)