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A136807
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Hankel transform of double factorial numbers n!*2^n=A000165(n).
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2
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1, 4, 256, 589824, 86973087744, 1282470362637926400, 2723154477021188283432960000, 1133321924829207204666583887642624000000, 120746421332702772771144114237731253721340313600000000
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OFFSET
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0,2
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COMMENTS
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By the properties of the Hankel transform, a(n)=2^(n(n+1))*A055209(n).
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LINKS
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FORMULA
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a(n) = Product_{k=1..n} (2k)^(2(n-k+1)).
a(n) ~ 2^((n+1)^2) * Pi^(n+1) * n^(n^2 + 2*n + 5/6) / (A^2 * exp(3*n^2/2 + 2*n - 1/6)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019
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MATHEMATICA
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Table[Product[(2k)^(2(n-k+1)), {k, n}], {n, 0, 10}] (* Harvey P. Dale, Apr 11 2013 *)
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PROG
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(PARI) for(n=0, 10, print1(prod(k=1, n, (2*k)^(2*(n-k+1))), ", ")) \\ G. C. Greubel, Oct 14 2018
(Magma) [1] cat [(&*[(2*k)^(2*(n-k+1)): k in [1..n]]): n in [1..10]]; // G. C. Greubel, Oct 14 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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