A389351 Expansion of (1/x) * Series_Reversion( x * (1 - x^3 / (1 - x)^5) ).

1, 0, 0, 1, 5, 15, 39, 115, 401, 1442, 5010, 17148, 59690, 212601, 765821, 2765884, 10015342, 36458835, 133517235, 491264537, 1813808525, 6717197381, 24952314005, 92964505756, 347283830492, 1300426565050, 4880160281498, 18351481294810, 69142169302872

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+2*k-1,n-3*k).

a(n) = (1/(n+1)) * [x^n] 1/(1 - x^3 / (1 - x)^5)^(n+1).

Mathematica

Table[SeriesCoefficient[1/(1-x^3/(1-x)^5)^(n+1), {x, 0, n}]/(n+1), {n, 0, 35}] (* Vincenzo Librandi, Oct 21 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x^3/(1-x)^5))/x)
(Magma) [1/(n+1)*&+[Binomial(n+k, k)*Binomial(n+2*k-1, n-3*k): k in [0..Floor(n/3)]]: n in [0..35]]; // Vincenzo Librandi, Oct 21 2025

Crossrefs

Cf. A389252.

Sequence in context: A099035 A262295 A034182 * A348885 A132985 A022570

Adjacent sequences: A389348 A389349 A389350 * A389352 A389353 A389354

Keyword

nonn

Author

Seiichi Manyama, Oct 01 2025

Status

approved