A034275 a(n) = f(n,n-2) where f is given in A034261.

1, 3, 14, 65, 294, 1302, 5676, 24453, 104390, 442442, 1864356, 7818538, 32657884, 135950700, 564306840, 2336457645, 9652643910, 39800950530, 163830074100, 673327275390, 2763494696820, 11327881630260, 46381659765480, 189711966348450, 775232392541724, 3165127107345252

Offset

1,2

Comments

Divisible by the Catalan numbers, by the explicit formula. - F. Chapoton, Jun 24 2021

Links

Table of n, a(n) for n=1..26.

Formula

a(n) = binomial(2*n-2,n-1)/n * (n^2-n+1).

a(n) = binomial(2*n-2,n-1) + (n-1)*binomial(2*n-2,n).

D-finite with recurrence n*a(n) + 2*(-6*n+7)*a(n-1) + 4*(11*n-24)*a(n-2) + 24*(-2*n+7)*a(n-3) = 0. - R. J. Mathar, Feb 10 2025

a(n) ~ 2^(2*n-2) * sqrt(n/Pi). - Amiram Eldar, Sep 04 2025

Mathematica

a[n_] := Binomial[2*n-2, n-1] * (n^2-n+1) / n; Array[a, 25] (* Amiram Eldar, Sep 04 2025 *)

Prog

(SageMath)
[binomial(2*n-2, n-1)//n * (n**2-n+1) for n in range(1, 8)]
(PARI) a(n) = binomial(2*n-2, n-1)/n * (n^2-n+1); \\ Michel Marcus, Jun 24 2021

Crossrefs

Cf. A000108, A002061, A034261, A344191, A344228.

Sequence in context: A161131 A247978 A026592 * A240008 A151322 A373450

Adjacent sequences: A034272 A034273 A034274 * A034276 A034277 A034278

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Corrected and extended by N. J. A. Sloane, Apr 21 2000

Status

approved