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a(n) = 2^(2*n)*(n!)^2*Product_{e_k} binomial(2*e_k, e_k) where 2n = Product p_k^e_k is the prime factorization of 2n.
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%I #7 Jan 07 2021 01:18:20

%S 8,384,9216,2949120,58982400,25480396800,1664719257600,

%T 7457942274048000,414235422307123200,165694168922849280000,

%U 26731992586219683840000,153976277296625378918400000,10408796345251875614883840000,24481489004032411446206791680000,14688893402419446867724075008000000

%N a(n) = 2^(2*n)*(n!)^2*Product_{e_k} binomial(2*e_k, e_k) where 2n = Product p_k^e_k is the prime factorization of 2n.

%H Floris P. van Doorn and Jasper Mulder, <a href="/A151932/b151932.txt">Table of n, a(n) for n = 1..250</a>.

%H Reinhardt Wiewe, <a href="http://en.wikipedia.org/w/index.php?oldid=305495518#Most-perfect_magic_square_.284.29">Most-perfect magic squares (4)</a>

%e n = 5: 2n = 10 = 2^1*5^1, a(5) = 2^10*120^2*2*2 = 58982400.

%t Array[2^(2#) (#!)^2 Times@@(Binomial[2#,# ]&/@FactorInteger[2# ][[All,2]])&,12] (* Floris P. van Doorn and Jasper Mulder (florisvandoorn(AT)hotmail.com), Oct 12 2009 *)

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Aug 11 2009

%E More terms from Floris P. van Doorn and Jasper Mulder (florisvandoorn(AT)hotmail.com), Oct 12 2009