A370055 a(n) = 3*(3*n+2)!/(2*n+3)!.

1, 3, 24, 330, 6552, 171360, 5581440, 218045520, 9945936000, 519177859200, 30535045632000, 1998518736614400, 144098325316915200, 11350405033583616000, 969837188805041356800, 89351761457237190912000, 8830056426362263572480000, 931769828125956695715840000

Offset

0,2

Links

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

Formula

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

a(n) = 3*A076151(n+1) for n > 0.

a(n) = A000142(n)*A001764(n+1). - Alois P. Heinz, Feb 08 2024

From Seiichi Manyama, Aug 31 2024: (Start)

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

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

E.g.f.: (1/x) * Series_Reversion( x/(1 + x)^3 ). - Seiichi Manyama, Feb 06 2025

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001763, A370054.

Cf. A065866, A370058.

Cf. A076151.

Cf. A000142, A001764.

Sequence in context: A375869 A082166 A354259 * A381443 A380808 A371007

Adjacent sequences: A370052 A370053 A370054 * A370056 A370057 A370058

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 08 2024

Status

approved