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%I #28 Dec 18 2022 02:32:41
%S 1,8,112,2240,58240,1863680,70819840,3116072960,155803648000,
%T 8725004288000,540950265856000,36784618078208000,2722061737787392000,
%U 217764939022991360000,18727784755977256960000,1722956197549907640320000,168849707359890948751360000
%N a(n) = n-th sextic factorial number divided by 2.
%H G. C. Greubel, <a href="/A034689/b034689.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 2*a(n) = (6*n-4)(!^6) = Product_{j=1..n} (6*j-4) = 2^n*A007559(n), A007559(n) = (3*n-2)(!^3) = Product_{j=1..n} (3*j-2).
%F E.g.f.: (-1 + (1-6*x)^(-1/3))/2).
%F D-finite with recurrence: a(n) = 2*(3*n-2)*a(n-1). - _R. J. Mathar_, Feb 24 2020
%F a(n) = 3*6^(n-1)*Pochhammer(n, 1/3). - _G. C. Greubel_, Oct 21 2022
%F From _Amiram Eldar_, Dec 18 2022: (Start)
%F a(n) = A047657(n)/2.
%F Sum_{n>=1} 1/a(n) = 2*(e/6^4)^(1/6)*(Gamma(1/3, 1/6) - Gamma(1/3)). (End)
%t Table[6^n*Pochhammer[1/3, n]/2, {n, 40}] (* _G. C. Greubel_, Oct 21 2022 *)
%o (Magma) [n le 1 select 1 else (6*n-4)*Self(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 21 2022
%o (SageMath) [6^n*rising_factorial(1/3,n)/2 for n in range(1,40)] # _G. C. Greubel_, Oct 21 2022
%Y Cf. A007559, A008542, A034723, A034724, A034787, A034788, A047657, A047058.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
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