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%I #31 Dec 18 2022 02:27:20
%S 1,10,160,3520,98560,3351040,134041600,6165913600,320627507200,
%T 18596395417600,1190169306726400,83311851470848000,
%U 6331700711784448000,519199458366324736000,45689552336236576768000,4294817919606238216192000,429481791960623821619200000
%N a(n) = n-th sextic factorial number divided by 4.
%H G. C. Greubel, <a href="/A034724/b034724.txt">Table of n, a(n) for n = 1..345</a>
%F 4*a(n) = (6*n-2)(!^6) = Product_{j=1..n} (6*j-2).
%F a(n) = 2^(n+1)*A034000(n), 2*A034000(n) = (3*n-1)(!^3).
%F E.g.f.: (-1 + (1-6*x)^(-2/3))/4.
%F D-finite with recurrence: a(n) +2*(-3*n+1)*a(n-1)=0. - _R. J. Mathar_, Jan 28 2020
%F Sum_{n>=1} 1/a(n) = 4*(e/6^2)^(1/6)*(Gamma(2/3) - Gamma(2/3, 1/6)). - _Amiram Eldar_, Dec 18 2022
%p seq( mul(6*j-2, j=1..n)/4, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t With[{nn=20},CoefficientList[Series[((1-6x)^(-2/3)-1)/4,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jun 02 2017 *)
%t Table[6^n*Pochhammer[2/3, n]/4, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o (PARI) vector(20, n, prod(j=1,n, 6*j-2)/4 ) \\ _G. C. Greubel_, Nov 11 2019
%o (Magma) [(&*[6*j-2: j in [1..n]])/4: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o (Sage) [product( (6*j-2) for j in (1..n))/4 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o (GAP) List([1..20], n-> Product([1..n], j-> 6*j-2)/4 ); # _G. C. Greubel_, Nov 11 2019
%Y Cf. A034000, A008542, A034689.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
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