A014298 a(n) = 2^n * (3n)! / (2n+1)!.

1, 2, 24, 576, 21120, 1048320, 65802240, 5000970240, 446557224960, 45830873088000, 5316381278208000, 687893507997696000, 98231192942070988800, 15345895252950201139200, 2603510504983275503616000, 476694375041453927694336000, 93692112621783944697741312000

Offset: 0

Author

Igor Pak

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Programs

GAP

List([0..20], n-> 2^n*Factorial(3*n)/Factorial(2*n+1) ); # G. C. Greubel, Jun 12 2019

Magma

[2^n*Factorial(3*n)/Factorial(2*n+1): n in [0..20]]; // G. C. Greubel, Jun 12 2019

Mathematica

Table[2^n (3n)!/(2n+1)!,{n,0,20}] (* Harvey P. Dale, Mar 19 2016 *)

PARI

a(n) = 2^n * (3*n)! / (2*n+1)! \\ Michel Marcus, Jun 24 2013

Sage

[2^n*factorial(3*n)/factorial(2*n+1) for n in (0..20)] # G. C. Greubel, Jun 12 2019

Formula

From G. C. Greubel, Jun 12 2019: (Start)

G.f.: Hypergeometric3F1(1/3, 2/3, 1; 3/2; 27*x/2).

E.g.f.: sqrt(2/(3*x)) * sin( arcsin(sqrt(27*x/2))/3 ).

E.g.f.: hypergeometric2F1(1/3, 2/3; 3/2; 27*x/2) (End)