A389411 Expansion of (1/x) * Series_Reversion( x * (1 - x) / (1 + x^3 / (1 - x)^3) ).

1, 1, 2, 6, 22, 87, 355, 1479, 6278, 27110, 118841, 527628, 2367675, 10720894, 48920913, 224735918, 1038509478, 4824103194, 22513668516, 105509641572, 496337349317, 2342869235037, 11093615574663, 52678904425461, 250805844200643, 1196978991435027, 5725377773004857

Offset

0,3

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

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

Mathematica

Table[SeriesCoefficient[((1+x^3/(1-x)^3)/(1-x))^(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)/(1+x^3/(1-x)^3))/x)
(Magma) [1/(n+1)*&+[Binomial(n+1, k)*Binomial(2*n, n-3*k): k in [0..Floor(n/3)]]: n in [0..30]]; // Vincenzo Librandi, Oct 17 2025

Crossrefs

Cf. A049128, A071969.

Cf. A389250.

Sequence in context: A165533 A164651 A279566 * A367413 A384829 A150261

Adjacent sequences: A389408 A389409 A389410 * A389412 A389413 A389414

Keyword

nonn

Author

Seiichi Manyama, Oct 03 2025

Status

approved