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A035018 One fifth of 9-factorial numbers.

%I A035018 #25 Dec 21 2022 04:45:53
%S A035018 1,14,322,10304,422464,21123200,1246268800,84746278400,6525463436800,
%T A035018 561189855564800,53313036278656000,5544555772980224000,
%U A035018 626534802346765312000,76437245886305368064000,10013279211106003216384000,1401859089554840450293760000,208877004343671227093770240000
%N A035018 One fifth of 9-factorial numbers.
%H A035018 G. C. Greubel, <a href="/A035018/b035018.txt">Table of n, a(n) for n = 1..325</a>
%H A035018 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A035018 5*a(n) = (9*n-4)(!^9) := Product_{j=1..n} (9*j-4).
%F A035018 E.g.f.: (-1+(1-9*x)^(-5/9))/5.
%F A035018 From _G. C. Greubel_, Oct 18 2022: (Start)
%F A035018 a(n) = (1/5) * 9^n * Pochhammer(n, 5/9).
%F A035018 a(n) = (9*n-4)*a(n-1). (End)
%F A035018 From _Amiram Eldar_, Dec 21 2022: (Start)
%F A035018 a(n) = A147629(n+1)/5.
%F A035018 Sum_{n>=1} 1/a(n) = 5*(e/9^4)^(1/9)*(Gamma(5/9) - Gamma(5/9, 1/9)). (End)
%t A035018 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 13, 2*5!, 9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t A035018 Rest[FoldList[Times,1,9*Range[20]-4]/5] (* _Harvey P. Dale_, May 22 2013 *)
%o A035018 (Magma) [n le 1 select 1 else (9*n-4)*Self(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 18 2022
%o A035018 (SageMath) [9^n*rising_factorial(5/9,n)/5 for n in range(1,40)] # _G. C. Greubel_, Oct 18 2022
%Y A035018 Cf. A007559, A034171, A035012, A035013, A035017, A035018.
%Y A035018 Cf. A035020, A035021, A035022, A035023, A045756, A147629.
%K A035018 easy,nonn
%O A035018 1,2
%A A035018 _Wolfdieter Lang_