%I #32 Sep 08 2022 08:44:52

%S 1,12,216,5184,155520,5598720,235146240,11287019520,609499054080,

%T 36569943244800,2413616254156800,173780370299289600,

%U 13554868883344588800,1138608986200945459200,102474808758085091328000,9837581640776168767488000,1003433327359169214283776000

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

%H G. C. Greubel, <a href="/A034788/b034788.txt">Table of n, a(n) for n = 1..345</a>

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

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

%F D-finite with recurrence: a(n) - 6*n*a(n-1) = 0. - _R. J. Mathar_, Feb 24 2020

%F From _Amiram Eldar_, Jan 08 2022: (Start)

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

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

%p seq(6^(n-1)*n!, n=1..20); # _G. C. Greubel_, Nov 11 2019

%t Table[6^(n-1)*n!,{n,20}] (* _Harvey P. Dale_, Dec 22 2013 *)

%o (PARI) vector(20, n, 6^(n-1)*n!) \\ _G. C. Greubel_, Nov 11 2019

%o (Magma) [6^(n-1)*Factorial(n): n in [1..20]]; // _G. C. Greubel_, Nov 11 2019

%o (Sage) [6^(n-1)*factorial(n) for n in (1..20)] # _G. C. Greubel_, Nov 11 2019

%o (GAP) List([1..20], n-> 6^(n-1)*Factorial(n) ); # _G. C. Greubel_, Nov 11 2019

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

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_