A365340 a(n) = (4*n)!/(3*n+1)!.

1, 1, 8, 132, 3360, 116280, 5100480, 271252800, 16963914240, 1220096908800, 99225500774400, 9003984596006400, 901928094049382400, 98856066097780992000, 11768525894839633920000, 1512185803617951221760000, 208598907329474462760960000

Offset: 0

Author

Seiichi Manyama, Sep 01 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A001761, A001763, A052795, A365341.

Cf. A004331, A061924.

Cf. A370056, A370057, A370058.

Cf. A000142, A002293.

Programs

PARI

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

Python

from sympy import ff
def A365340(n): return ff(n<<2,n-1) # Chai Wah Wu, Sep 01 2023

Formula

E.g.f.: exp( 1/4 * Sum_{k>=1} binomial(4*k,k) * x^k/k ). - Seiichi Manyama, Feb 08 2024

a(n) = A000142(n)*A002293(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)^3).

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