A389248 Expansion of (1/x) * Series_Reversion( x / (1 + x^2 / (1 - x)^5) ).

1, 0, 1, 5, 17, 60, 240, 1001, 4204, 17919, 77762, 341990, 1518913, 6804421, 30718935, 139616100, 638261250, 2932960734, 13540120577, 62768552380, 292070800676, 1363670247150, 6386678710051, 29996530467849, 141252737962111, 666751617147950, 3154235587997925

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(n+3*k-1,n-2*k).

a(n) = (1/(n+1)) * [x^n] (1 + x^2 / (1 - x)^5)^(n+1).

Mathematica

a[n_]:=SeriesCoefficient[(1+x^2/(1-x)^5)^(n+1), {x, 0, n}]/(n+1); Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, Oct 01 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x^2/(1-x)^5))/x)
(Magma) a := [ n eq 0 select 1 else &+[Binomial(n+1, k) * Binomial(n+3*k-1, n-2*k) : k in [0..Floor(n/2)] ] div (n+1) : n in [0..30] ]; a; // Vincenzo Librandi, Oct 01 2025

Crossrefs

Cf. A321799, A389252.

Sequence in context: A149661 A146130 A026619 * A142956 A273422 A192146

Adjacent sequences: A389245 A389246 A389247 * A389249 A389250 A389251

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2025

Status

approved