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

0,2

Links

Table of n, a(n) for n=0..17.

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)

a(n) ~ 3^(3*n+3/2) * n^(n-1) / (2^(2*n+3/2) * exp(n+7/(6*n))). - Amiram Eldar, Nov 07 2025

Mathematica

a[n_] := 2*(3*n+1)!/(2*n+2)!; Array[a, 20, 0] (* Amiram Eldar, Nov 07 2025 *)

Prog

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

Crossrefs

Cf. A001763, A370055.

Cf. A000142, A006013.

Sequence in context: A396589 A285270 A109520 * A210097 A230991 A381387

Adjacent sequences: A370051 A370052 A370053 * A370055 A370056 A370057

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 08 2024

Status

approved