A065424 Catalan-like formula: a(n) = binomial(6*n, 3*n+1)/(9*n+6).

1, 33, 1326, 59432, 2851425, 143291610, 7446255180, 396893583792, 21579377870484, 1192183281903845, 66734212415276406, 3776778437640143208, 215744630060724034270, 12423227699242323077940, 720356761939547257421400, 42024927437494196952957408, 2464931252806478840545733484

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Formula

G.f.: A*sqrt((A+1)*(1+9*A)) where A=x*(1+9*A)^3*(1+A). - Mark van Hoeij, Nov 16 2011

-(n-1)*(3*n+2)*(3*n+1)*a(n) + 8*(6*n-5)*(6*n-1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Oct 31 2015

a(n) = (1/9)*A000245(3*n) = n*A000108(3*n)/(3*n + 2) for n >= 1. - Peter Bala, Mar 08 2023

a(n) ~ 2^(6*n) / (9 * sqrt(3*Pi) * n^(3/2)). - Amiram Eldar, Sep 04 2025

Mathematica

a[n_] := Binomial[6*n, 3*n+1]/(9*n+6); Array[a, 20] (* Amiram Eldar, Sep 04 2025 *)

Prog

(Magma) [Binomial(6*n, 3*n+1)/(9*n+6): n in [1..20]]; // Vincenzo Librandi, Nov 17 2011

Crossrefs

Cf. A000108, A000245, A065097.

Sequence in context: A353114 A294436 A242492 * A071268 A012805 A093756

Adjacent sequences: A065421 A065422 A065423 * A065425 A065426 A065427

Keyword

nonn,easy

Author

Len Smiley, Nov 16 2001

Status

approved