A218441 a(n) = A000108(n)*A001764(n).

1, 1, 6, 60, 770, 11466, 188496, 3325608, 61866090, 1199333850, 24030289140, 494663027040, 10414559269296, 223487031938800, 4874879691748800, 107852781825352080, 2415945569351185530, 54714061423541554650, 1251237165698155135500, 28864572348777684057000

Offset: 0

Author

Paul D. Hanna, Oct 28 2012

Keywords

• nonn
• easy

Comments

G.f. of A000108, C(x), satisfies: C(x) = 1 + x*C(x)^2;

G.f. of A001764, F(x), satisfies: F(x) = 1 + x*F(x)^3.

Examples

			G.f.: A(x) = 1 + x + 6*x^2 + 60*x^3 + 770*x^4 + 11466*x^5 + 188496*x^6 + ...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..705

Crossrefs

Cf. A000108, A001764, A086201.

Programs

Mathematica

a[n_] := CatalanNumber[n] * Binomial[3*n, n]/(2*n+1); Array[a, 20, 0] (* Amiram Eldar, Apr 26 2025 *)

Maxima

A218441[n]:=binomial(2*n, n)/(n+1)*binomial(3*n, n)/(2*n+1)$
makelist(A218441[n],n,0,30); /* Martin Ettl, Oct 29 2012 */

PARI

{a(n)=binomial(2*n,n)/(n+1)*binomial(3*n,n)/(2*n+1)}
for(n=0,25,print1(a(n),", "))

Formula

a(n) ~ 3^(3*n+1/2)/(2*Pi*n*(n+1)*(2*n+1)) = A086201*3^(3*n+1/2)/(n*(n+1)*(2*n+1)) (using the Stirling approximation for n!). - A.H.M. Smeets, Dec 31 2022