A387777 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3*(1+x)^3)) ).

1, 2, 5, 15, 55, 237, 1112, 5383, 26315, 129455, 642326, 3221550, 16339102, 83714139, 432596925, 2251277128, 11785224610, 62010358212, 327766828938, 1739615154595, 9267650140954, 49541732291450, 265661128574881, 1428643252250679, 7702926103476808, 41632599194983867, 225516188040424469

Offset

0,2

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

a(n) = (1/(n+1)) * [x^n] ((1+x)^2 * (1+x^3*(1+x)^3))^(n+1).

Mathematica

Table[(1/(n+1)) Coefficient[((1+x)^2*(1+x^3*(1+x)^3))^(n+1), x, n], {n, 0, 35}] (* Vincenzo Librandi, Oct 21 2025 *)

Prog

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

Crossrefs

Cf. A389064, A389158.

Sequence in context: A394998 A104429 A109319 * A387671 A059219 A242275

Adjacent sequences: A387774 A387775 A387776 * A387778 A387779 A387780

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2025

Status

approved