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

Author

Clark Kimberling

Keywords

• nonn
• easy
• changed

Comments

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

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = binomial(2*n-2,n-1)/n * (n^2-n+1); \\ Michel Marcus, Jun 24 2021

Sage

[binomial(2*n-2,n-1)//n * (n**2-n+1) for n in range(1,8)]

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

Extensions

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