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
Links
- G. C. Greubel, Table of n, a(n) for n = 1..345
Programs
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GAP
List([1..20], n-> 6^(n-1)*Factorial(n) ); # G. C. Greubel, Nov 11 2019
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Magma
[6^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Nov 11 2019
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Maple
seq(6^(n-1)*n!, n=1..20); # G. C. Greubel, Nov 11 2019
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Mathematica
Table[6^(n-1)*n!,{n,20}] (* Harvey P. Dale, Dec 22 2013 *) -
PARI
vector(20, n, 6^(n-1)*n!) \\ G. C. Greubel, Nov 11 2019
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Sage
[6^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Nov 11 2019
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)