A389251 - OEIS

A389251

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

1, 0, 0, 1, 4, 10, 23, 63, 200, 636, 1950, 5951, 18579, 59228, 190281, 612508, 1979024, 6433208, 21034032, 69067413, 227542366, 751996934, 2493060757, 8289425078, 27634504807, 92342177900, 309240130680, 1037723583000, 3488984948241, 11751382151394, 39645877077820

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

OFFSET

0,5

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(n+k-1,n-3*k).

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

MATHEMATICA

a[n_]:=SeriesCoefficient[(1+x^3/(1-x)^4)^(n+1), {x, 0, n}]/(n+1); Table[a[n], {n, 0, 35}] (* Vincenzo Librandi, Oct 03 2025 *)

PROG

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