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%I #17 Sep 08 2022 08:44:39
%S 1,2,24,576,21120,1048320,65802240,5000970240,446557224960,
%T 45830873088000,5316381278208000,687893507997696000,
%U 98231192942070988800,15345895252950201139200,2603510504983275503616000,476694375041453927694336000,93692112621783944697741312000
%N a(n) = 2^n * (3n)! / (2n+1)!.
%H G. C. Greubel, <a href="/A014298/b014298.txt">Table of n, a(n) for n = 0..250</a>
%F From _G. C. Greubel_, Jun 12 2019: (Start)
%F G.f.: Hypergeometric3F1(1/3, 2/3, 1; 3/2; 27*x/2).
%F E.g.f.: sqrt(2/(3*x)) * sin( arcsin(sqrt(27*x/2))/3 ).
%F E.g.f.: hypergeometric2F1(1/3, 2/3; 3/2; 27*x/2) (End)
%t Table[2^n (3n)!/(2n+1)!,{n,0,20}] (* _Harvey P. Dale_, Mar 19 2016 *)
%o (PARI) a(n) = 2^n * (3*n)! / (2*n+1)! \\ _Michel Marcus_, Jun 24 2013
%o (Magma) [2^n*Factorial(3*n)/Factorial(2*n+1): n in [0..20]]; // _G. C. Greubel_, Jun 12 2019
%o (Sage) [2^n*factorial(3*n)/factorial(2*n+1) for n in (0..20)] # _G. C. Greubel_, Jun 12 2019
%o (GAP) List([0..20], n-> 2^n*Factorial(3*n)/Factorial(2*n+1) ) # _G. C. Greubel_, Jun 12 2019
%K nonn,easy
%O 0,2
%A _Igor Pak_
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