A034325 a(n) is the n-th quintic factorial number divided by 5.
1, 10, 150, 3000, 75000, 2250000, 78750000, 3150000000, 141750000000, 7087500000000, 389812500000000, 23388750000000000, 1520268750000000000, 106418812500000000000, 7981410937500000000000, 638512875000000000000000
Offset: 1
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..354
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 594.
- Norihiro Nakashima and Shuhei Tsujie, Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species, arXiv:1904.09748 [math.CO], 2019.
Programs
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GAP
List([1..20], n-> 5^(n-1)*Factorial(n) ); # G. C. Greubel, Aug 23 2019
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Magma
[5^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 23 2019
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Maple
seq(5^(n-1)*n!, n=1..20); # G. C. Greubel, Aug 23 2019
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Mathematica
Array[5^(# - 1) #! &, 16] (* Michael De Vlieger, May 30 2019 *)
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PARI
vector(20, n, 5^(n-1)*n!) \\ G. C. Greubel, Aug 23 2019
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Sage
[5^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Aug 23 2019
Formula
5*a(n) = (5*n)(!^5) = Product_{j=1..n} 5*j = 5^(n-1)*n!.
E.g.f.: (-1 + (1-5*x)^(-1))/5, a(0) = 0.
D-finite with recurrence: a(n) - 5*n*a(n-1) = 0. - R. J. Mathar, Feb 24 2020
From Amiram Eldar, Jan 08 2022: (Start)
Sum_{n>=1} 1/a(n) = 5*(exp(1/5)-1).
Sum_{n>=1} (-1)^(n+1)/a(n) = 5*(1-exp(-1/5)). (End)