A034788 a(n) is the n-th sextic factorial number divided by 6.

1, 12, 216, 5184, 155520, 5598720, 235146240, 11287019520, 609499054080, 36569943244800, 2413616254156800, 173780370299289600, 13554868883344588800, 1138608986200945459200, 102474808758085091328000, 9837581640776168767488000, 1003433327359169214283776000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..345

Formula

6*a(n) = (6*n)(!^6) = Product_{j=1..n} 6*j = 6^n*n!.

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

D-finite with recurrence: a(n) - 6*n*a(n-1) = 0. - R. J. Mathar, Feb 24 2020

From Amiram Eldar, Jan 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 6*(exp(1/6)-1).

Sum_{n>=1} (-1)^(n+1)/a(n) = 6*(1-exp(-1/6)). (End)

Maple

seq(6^(n-1)*n!, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Table[6^(n-1)*n!, {n, 20}] (* Harvey P. Dale, Dec 22 2013 *)

Prog

(PARI) vector(20, n, 6^(n-1)*n!) \\ G. C. Greubel, Nov 11 2019
(Magma) [6^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Nov 11 2019
(Sage) [6^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) List([1..20], n-> 6^(n-1)*Factorial(n) ); # G. C. Greubel, Nov 11 2019

Crossrefs

Cf. A008542, A034689, A034723, A034724, A034787.

Sequence in context: A268369 A091266 A119309 * A082165 A006689 A009176

Adjacent sequences: A034785 A034786 A034787 * A034789 A034790 A034791

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved