A370056 a(n) = 2*(4*n+1)!/(3*n+2)!.

1, 2, 18, 312, 8160, 287280, 12751200, 684028800, 43062243840, 3113350732800, 254265345734400, 23153103246873600, 2326025084653670400, 255579097716214272000, 30491180727539051520000, 3925248256199788277760000, 542357159056633603178496000

Offset: 0

Author

Seiichi Manyama, Feb 08 2024

Keywords

• nonn

Crossrefs

Cf. A365340, A370057, A370058.

Cf. A000142, A069271.

Programs

PARI

a(n) = 2*(4*n+1)!/(3*n+2)!;

Formula

E.g.f.: exp( 1/2 * Sum_{k>=1} binomial(4*k,k) * x^k/k ).

a(n) = A000142(n) * A069271(n).

D-finite with recurrence 3*(3*n+2)*(3*n+1)*a(n) -8*(4*n+1)*(2*n-1)*(4*n-1)*a(n-1)=0. - R. J. Mathar, Feb 22 2024

From Seiichi Manyama, Aug 31 2024: (Start)

E.g.f. satisfies A(x) = 1/(1 - x*A(x)^(3/2))^2.

a(n) = 2 * Sum_{k=0..n} (3*n+2)^(k-1) * |Stirling1(n,k)|. (End)