A389660 Expansion of (1/x) * Series_Reversion( x * (1 - x * (1 + x)^2)^2 ).

1, 2, 11, 68, 473, 3510, 27251, 218586, 1797267, 15067316, 128307685, 1106775150, 9650428107, 84920021864, 753171175532, 6725897514182, 60424766404011, 545740764344752, 4952362528273121, 45131545826450266, 412865243836628363, 3790014882563926310, 34901419463705667915

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

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

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

Mathematica

Table[SeriesCoefficient[1/(1-x*(1+x)^2)^(2*(n+1)), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 20 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x*(1+x)^2)^2)/x)
(Magma) [1/(n+1)*&+[Binomial(2*n+k+1, k)*Binomial(2*k, n-k): k in [0..n]]: n in [0..35]]; // Vincenzo Librandi, Oct 20 2025

Crossrefs

Cf. A368961.

Sequence in context: A153298 A153393 A365135 * A274736 A361410 A229230

Adjacent sequences: A389657 A389658 A389659 * A389661 A389662 A389663

Keyword

nonn

Author

Seiichi Manyama, Oct 10 2025

Status

approved