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A035017 One quarter of 9-factorial numbers.

%I A035017 #22 Dec 21 2022 04:45:48
%S A035017 1,13,286,8866,354640,17377360,1007886880,67528420960,5132159992960,
%T A035017 436233599401600,41005958343750400,4223613709406291200,
%U A035017 473044735453504614400,57238412989874058342400,7440993688683627584512000,1034298122727024234247168000,153076122163599586668580864000
%N A035017 One quarter of 9-factorial numbers.
%H A035017 G. C. Greubel, <a href="/A035017/b035017.txt">Table of n, a(n) for n = 1..325</a>
%H A035017 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A035017 4*a(n) = (9*n-5)(!^9) := Product_{j=1..n} (9*j-5).
%F A035017 E.g.f.: (-1+(1-9*x)^(-4/9))/4.
%F A035017 From _G. C. Greubel_, Oct 18 2022: (Start)
%F A035017 a(n) = (1/4) * 9^n * Pochhammer(n, 4/9).
%F A035017 a(n) = (9*n-5)*a(n-1). (End)
%F A035017 From _Amiram Eldar_, Dec 21 2022: (Start)
%F A035017 a(n) = A144829(n)/4.
%F A035017 Sum_{n>=1} 1/a(n) = 4*(e/9^5)^(1/9)*(Gamma(4/9) - Gamma(4/9, 1/9)). (End)
%t A035017 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 12, 2*5!, 9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t A035017 Table[9^n*Pochhammer[4/9, n]/4, {n,40}] (* _G. C. Greubel_, Oct 18 2022 *)
%o A035017 (Magma) [n le 1 select 1 else (9*n-5)*Self(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 18 2022
%o A035017 (SageMath) [9^n*rising_factorial(4/9,n)/4 for n in range(1,40)] # _G. C. Greubel_, Oct 18 2022
%Y A035017 Cf. A007559, A034171, A035012, A035013, A035017, A035018.
%Y A035017 Cf. A035020, A035021, A035022, A035023, A045756, A144829.
%K A035017 easy,nonn
%O A035017 1,2
%A A035017 _Wolfdieter Lang_