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%I #37 Dec 20 2022 03:51:24
%S 1,13,273,7917,292929,13181805,698635665,42616775565,2940557513985,
%T 226422928576845,19245948929031825,1789873250399959725,
%U 180777198290395932225,19704714613653156612525,2305451609797419323665425,288181451224677415458178125,38328133012882096255937690625
%N One fifth of octo-factorial numbers.
%H G. C. Greubel, <a href="/A034911/b034911.txt">Table of n, a(n) for n = 1..325</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F 5*a(n) = (8*n-3)(!^8) = Product_{j=1..n} 8*j-3.
%F E.g.f.: (-1+(1-8*x)^(-5/8))/5.
%F 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
%F D-finite with recurrence: a(n) = (8*n-3)*a(n-1). - _R. J. Mathar_, Jan 28 2020
%F a(n) = (1/5)* 8^n * Pochhammer(n, 5/8). - _G. C. Greubel_, Oct 20 2022
%F From _Amiram Eldar_, Dec 20 2022: (Start)
%F a(n) = A147625(n+1)/5.
%F Sum_{n>=1} 1/a(n) = 5*(e/8^3)^(1/8)*(Gamma(5/8) - Gamma(5/8, 1/8)). (End)
%t 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 *)
%o (Magma) [n le 1 select 1 else (8*n-3)*Self(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 20 2022
%o (SageMath) [8^n*rising_factorial(5/8,n)/5 for n in range(1,40)] # _G. C. Greubel_, Oct 20 2022
%Y Cf. A034908, A034909, A034910, A034911, A034912, A045755, A147625.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
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