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A062029
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Group even numbers into (2), (4,6), (8,10,12), (14,16,18,20), ...; a(n) = product of n-th group.
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4
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2, 24, 960, 80640, 11531520, 2500485120, 763847884800, 312344808652800, 164644289755545600, 108684799028822016000, 87805845811395506995200, 85211145316323008446464000, 97803969545162680178835456000
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OFFSET
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1,1
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LINKS
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FORMULA
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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).
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EXAMPLE
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a(3) = 8*10*12 = 960.
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MATHEMATICA
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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 *)
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PROG
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(PARI) { for (n=1, 60, write("b062029.txt", 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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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