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

0,3

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.

Links

Table of n, a(n) for n=0..19.

Formula

Using the Stirling approximation for n! we get the asymptotic expansion 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)). - A.H.M. Smeets, Dec 31 2022

Example

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

Prog

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

Crossrefs

Cf. A000108, A001764.

Sequence in context: A065944 A357771 A126779 * A120973 A259606 A302102

Adjacent sequences: A218438 A218439 A218440 * A218442 A218443 A218444

Keyword

nonn

Author

Paul D. Hanna, Oct 28 2012

Status

approved