A370054 a(n) = 2*(3*n+1)!/(2*n+2)!.

1, 2, 14, 180, 3432, 87360, 2790720, 107442720, 4845456000, 250637587200, 14631376032000, 951675588864000, 68257101465907200, 5352223511771136000, 455529588681155788800, 41824228767217408512000, 4120692998969056333824000, 433653882272457833226240000

Offset: 0

Author

Seiichi Manyama, Feb 08 2024

Keywords

• nonn

Crossrefs

Cf. A001763, A370055.

Cf. A000142, A006013.

Programs

PARI

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

Formula

E.g.f.: exp( 2/3 * Sum_{k>=1} binomial(3*k,k) * x^k/k ).

a(n) = A000142(n)*A006013(n). - Alois P. Heinz, Feb 08 2024

From Seiichi Manyama, Aug 31 2024: (Start)

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

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