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A035020 One sixth of 9-factorial numbers.

%I A035020 #24 Dec 21 2022 08:19:05
%S A035020 1,15,360,11880,498960,25446960,1526817600,105350414400,8217332323200,
%T A035020 714907912118400,68631159563366400,7206271754153472000,
%U A035020 821514979973495808000,101046342536739984384000,13338117214849677938688000,1880674527293804589355008000,282101179094070688403251200000
%N A035020 One sixth of 9-factorial numbers.
%H A035020 G. C. Greubel, <a href="/A035020/b035020.txt">Table of n, a(n) for n = 1..325</a>
%H A035020 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A035020 6*a(n) = (9*n-3)(!^9) := Product_{j=1..n} (9*j-3) = 3^n*2*A034000(n), where 2*A034000(n) = (3*n-1)(!^3) := Product_{j=1..n} (3*j-1).
%F A035020 E.g.f.: (-1+(1-9*x)^(-2/3))/6.
%F A035020 From _G. C. Greubel_, Oct 18 2022: (Start)
%F A035020 a(n) = (1/6) * 9^n * Pochhammer(n, 2/3).
%F A035020 a(n) = (9*n - 3)*a(n-1). (End)
%F A035020 From _Amiram Eldar_, Dec 21 2022: (Start)
%F A035020 a(n) = A147630(n+1)/6.
%F A035020 Sum_{n>=1} 1/a(n) = 6*(e/9^3)^(1/9)*(Gamma(2/3) - Gamma(2/3, 1/9)). (End)
%t A035020 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 14, 2*5!, 9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t A035020 Table[9^n*Pochhammer[2/3, n]/6, {n, 40}] (* _G. C. Greubel_, Oct 18 2022 *)
%o A035020 (Magma) [n le 1 select 1 else (9*n-3)*Self(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 18 2022
%o A035020 (SageMath) [9^n*rising_factorial(2/3,n)/6 for n in range(1,40)] # _G. C. Greubel_, Oct 18 2022
%Y A035020 Cf. A007559, A034000, A034171, A035012, A035013, A035017, A147630.
%Y A035020 Cf. A035018, A035020, A035021, A035022, A035023, A045756.
%K A035020 easy,nonn
%O A035020 1,2
%A A035020 _Wolfdieter Lang_