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URL: https://oeis.org/A062029

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A062029
Group even numbers into (2), (4,6), (8,10,12), (14,16,18,20), ...; a(n) = product of n-th group.
4
2, 24, 960, 80640, 11531520, 2500485120, 763847884800, 312344808652800, 164644289755545600, 108684799028822016000, 87805845811395506995200, 85211145316323008446464000, 97803969545162680178835456000, 131047222390590123375392194560000, 202702319752278628965061257854976000
OFFSET
1,1
LINKS
FORMULA
a(n) = Product_{k=1..n} (n^2 - n + 2*k) = (n^2 + n)!!/(n^2 - n)!! .
a(n) = 2^n*Gamma((n^2 + n + 2)/2)/Gamma((n^2 - n + 2)/2).
a(n) = 2^n * A057003(n-1).
EXAMPLE
a(3) = 8*10*12 = 960.
MATHEMATICA
Table[2^n*Gamma[(2+n+n^2)/2]/Gamma[(2-n+n^2)/2], {n, 30}] (* G. C. Greubel, May 05 2022 *)
With[{nn=30}, Times@@@TakeList[Range[2, (nn(nn+1))/2, 2], Range[nn/2]]] (* Harvey P. Dale, May 09 2022 *)
PROG
(PARI) a(n) = { 2^n*((n^2 + n)/2)!/((n^2 - n)/2)! } \\ Harry J. Smith, Jul 30 2009
(SageMath) [2^n*gamma((2+n+n^2)/2)/gamma((2-n+n^2)/2) for n in (1..30)] # G. C. Greubel, May 05 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 02 2001
EXTENSIONS
Formula and more terms from Vladeta Jovovic, Jun 05 2001
STATUS
approved