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

1,2

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.

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)

Maple

seq(5^(n-1)*n!, n=1..20); # G. C. Greubel, Aug 23 2019

Mathematica

Array[5^(# - 1) #! &, 16] (* Michael De Vlieger, May 30 2019 *)

Prog

(PARI) vector(20, n, 5^(n-1)*n!) \\ G. C. Greubel, Aug 23 2019
(Magma) [5^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 23 2019
(Sage) [5^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Aug 23 2019
(GAP) List([1..20], n-> 5^(n-1)*Factorial(n) ); # G. C. Greubel, Aug 23 2019

Crossrefs

Cf. A008548, A034300, A034301, A034323, A052562.

Sequence in context: A212472 A025750 A365622 * A335800 A239620 A253124

Adjacent sequences: A034322 A034323 A034324 * A034326 A034327 A034328

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved