A034689 a(n) = n-th sextic factorial number divided by 2.

1, 8, 112, 2240, 58240, 1863680, 70819840, 3116072960, 155803648000, 8725004288000, 540950265856000, 36784618078208000, 2722061737787392000, 217764939022991360000, 18727784755977256960000, 1722956197549907640320000, 168849707359890948751360000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..325

Index entries for sequences related to factorial numbers.

Formula

2*a(n) = (6*n-4)(!^6) = Product_{j=1..n} (6*j-4) = 2^n*A007559(n), A007559(n) = (3*n-2)(!^3) = Product_{j=1..n} (3*j-2).

E.g.f.: (-1 + (1-6*x)^(-1/3))/2).

D-finite with recurrence: a(n) = 2*(3*n-2)*a(n-1). - R. J. Mathar, Feb 24 2020

a(n) = 3*6^(n-1)*Pochhammer(n, 1/3). - G. C. Greubel, Oct 21 2022

From Amiram Eldar, Dec 18 2022: (Start)

a(n) = A047657(n)/2.

Sum_{n>=1} 1/a(n) = 2*(e/6^4)^(1/6)*(Gamma(1/3, 1/6) - Gamma(1/3)). (End)

Mathematica

Table[6^n*Pochhammer[1/3, n]/2, {n, 40}] (* G. C. Greubel, Oct 21 2022 *)

Prog

(Magma) [n le 1 select 1 else (6*n-4)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 21 2022
(SageMath) [6^n*rising_factorial(1/3, n)/2 for n in range(1, 40)] # G. C. Greubel, Oct 21 2022

Crossrefs

Cf. A007559, A008542, A034723, A034724, A034787, A034788, A047657, A047058.

Sequence in context: A265665 A302104 A219184 * A010041 A099703 A296467

Adjacent sequences: A034686 A034687 A034688 * A034690 A034691 A034692

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved