A389441 - OEIS

A389441

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

1, 1, 1, 2, 9, 37, 125, 394, 1318, 4819, 18233, 68498, 255405, 959469, 3658197, 14105139, 54676054, 212590108, 829729478, 3253606934, 12815186231, 50657719421, 200837879181, 798401660056, 3182297592982, 12715843227373, 50926223937385, 204379765181156

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

OFFSET

0,4

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+3*k+1,n-3*k).

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

MATHEMATICA

Table[SeriesCoefficient[((1+x)/(1-x^3*(1+x)^3))^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 17 2025 *)

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x^3*(1+x)^3)/(1+x))/x)