A034911 One fifth of octo-factorial numbers.

1, 13, 273, 7917, 292929, 13181805, 698635665, 42616775565, 2940557513985, 226422928576845, 19245948929031825, 1789873250399959725, 180777198290395932225, 19704714613653156612525, 2305451609797419323665425, 288181451224677415458178125, 38328133012882096255937690625

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..325
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A034908, A034909, A034910, A034911, A034912, A045755, A147625.

Programs

Magma

[n le 1 select 1 else (8*n-3)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 20 2022

Mathematica

With[{nn=20},CoefficientList[Series[(-1+(1-8x)^(-5/8))/5,{x,0,nn}],x] Range[0,nn]!] (* or *) FoldList[Times,Range[5,200,8]]/5 (* Harvey P. Dale, May 25 2016 *)

SageMath

[8^n*rising_factorial(5/8,n)/5 for n in range(1,40)] # G. C. Greubel, Oct 20 2022

Formula

5*a(n) = (8*n-3)(!^8) = Product_{j=1..n} 8*j-3.

E.g.f.: (-1+(1-8*x)^(-5/8))/5.

G.f.: x/(1-13*x/(1-8*x/(1-21*x/(1-16*x/(1-29*x/(1-24*x/(1-37*x/(1-32*x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012

D-finite with recurrence: a(n) = (8*n-3)*a(n-1). - R. J. Mathar, Jan 28 2020

a(n) = (1/5)* 8^n * Pochhammer(n, 5/8). - G. C. Greubel, Oct 20 2022

From Amiram Eldar, Dec 20 2022: (Start)

a(n) = A147625(n+1)/5.

Sum_{n>=1} 1/a(n) = 5*(e/8^3)^(1/8)*(Gamma(5/8) - Gamma(5/8, 1/8)). (End)