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A034724
a(n) = n-th sextic factorial number divided by 4.
12
1, 10, 160, 3520, 98560, 3351040, 134041600, 6165913600, 320627507200, 18596395417600, 1190169306726400, 83311851470848000, 6331700711784448000, 519199458366324736000, 45689552336236576768000, 4294817919606238216192000, 429481791960623821619200000
OFFSET
1,2
LINKS
FORMULA
4*a(n) = (6*n-2)(!^6) = Product_{j=1..n} (6*j-2).
a(n) = 2^(n+1)*A034000(n), 2*A034000(n) = (3*n-1)(!^3).
E.g.f.: (-1 + (1-6*x)^(-2/3))/4.
D-finite with recurrence: a(n) +2*(-3*n+1)*a(n-1)=0. - R. J. Mathar, Jan 28 2020
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
MAPLE
seq( mul(6*j-2, j=1..n)/4, n=1..20); # G. C. Greubel, Nov 11 2019
MATHEMATICA
With[{nn=20}, CoefficientList[Series[((1-6x)^(-2/3)-1)/4, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 02 2017 *)
Table[6^n*Pochhammer[2/3, n]/4, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)
PROG
(PARI) vector(20, n, prod(j=1, n, 6*j-2)/4 ) \\ G. C. Greubel, Nov 11 2019
(Magma) [(&*[6*j-2: j in [1..n]])/4: n in [1..20]]; // G. C. Greubel, Nov 11 2019
(Sage) [product( (6*j-2) for j in (1..n))/4 for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) List([1..20], n-> Product([1..n], j-> 6*j-2)/4 ); # G. C. Greubel, Nov 11 2019
CROSSREFS
KEYWORD
easy,nonn
STATUS
approved