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A147625 Octo-factorial numbers(4). 5

%I

%S 1,5,65,1365,39585,1464645,65909025,3493178325,213083877825,

%T 14702787569925,1132114642884225,96229744645159125,

%U 8949366251999798625,903885991451979661125,98523573068265783062625

%N Octo-factorial numbers(4).

%F a(n+1) = Sum_{k, 0<=k<=n}A132393(n,k)*5^k*8^(n-k). [_Philippe Deléham_, Nov 09 2008]

%F a(n) = (-3)^n*sum_{k=0..n} (8/3)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. [_Mircea Merca_, May 03 2012]

%F a(n) +(-8*n+11)*a(n-1)=0. - _R. J. Mathar_, Sep 04 2016

%F From _Benedict W. J. Irwin_, Sep 30 2016: (Start)

%F a(n) = Product_{k=0..n-1} 8*k+5.

%F a(n) = 8^n*Gamma(5/8 + n)/Gamma(5/8).

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

%F (End)

%F a(n)/n! ~ 8^n/(Gamma(5/8)*n^(3/8)). - _Vaclav Kotesovec_, Oct 04 2016

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst,s],{n,4,2*5!,8}];lst

%t Table[Product[(8k+5), {k, 0, n-1}], {n, 0, 20} (* _Benedict W. J. Irwin_, Sep 30 2016 *)

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)