cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A034788 #32 Sep 08 2022 08:44:52
%S A034788 1,12,216,5184,155520,5598720,235146240,11287019520,609499054080,
%T A034788 36569943244800,2413616254156800,173780370299289600,
%U A034788 13554868883344588800,1138608986200945459200,102474808758085091328000,9837581640776168767488000,1003433327359169214283776000
%N A034788 a(n) is the n-th sextic factorial number divided by 6.
%H A034788 G. C. Greubel, <a href="/A034788/b034788.txt">Table of n, a(n) for n = 1..345</a>
%F A034788 6*a(n) = (6*n)(!^6) = Product_{j=1..n} 6*j = 6^n*n!.
%F A034788 E.g.f.: (-1 + 1/(1-6*x))/6.
%F A034788 D-finite with recurrence: a(n) - 6*n*a(n-1) = 0. - _R. J. Mathar_, Feb 24 2020
%F A034788 From _Amiram Eldar_, Jan 08 2022: (Start)
%F A034788 Sum_{n>=1} 1/a(n) = 6*(exp(1/6)-1).
%F A034788 Sum_{n>=1} (-1)^(n+1)/a(n) = 6*(1-exp(-1/6)). (End)
%p A034788 seq(6^(n-1)*n!, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t A034788 Table[6^(n-1)*n!,{n,20}] (* _Harvey P. Dale_, Dec 22 2013 *)
%o A034788 (PARI) vector(20, n, 6^(n-1)*n!) \\ _G. C. Greubel_, Nov 11 2019
%o A034788 (Magma) [6^(n-1)*Factorial(n): n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o A034788 (Sage) [6^(n-1)*factorial(n) for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o A034788 (GAP) List([1..20], n-> 6^(n-1)*Factorial(n) ); # _G. C. Greubel_, Nov 11 2019
%Y A034788 Cf. A008542, A034689, A034723, A034724, A034787.
%K A034788 easy,nonn
%O A034788 1,2
%A A034788 _Wolfdieter Lang_