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a(n) = (n + 1/3) * (3*n + 3)! / ((n + 1)!)^3.
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%I #4 Feb 15 2023 07:12:11

%S 2,120,3920,115500,3279276,91483392,2527462080,69413752980,

%T 1898945262500,51809303385840,1410778953118080,38360293308573600,

%U 1041896542898685600,28274302212143040000,766761376923703054080,20781963787558897929060,563007692048242597348500,15246741943087253044446000

%N a(n) = (n + 1/3) * (3*n + 3)! / ((n + 1)!)^3.

%p a := n -> (n + 1/3)*(3*n + 3)!/(n + 1)!^3: seq(a(n), n = 0..17);

%Y Family: A000027 (m=1), A257589 (m=2), this sequence (m=3).

%K nonn

%O 0,1

%A _Peter Luschny_, Feb 15 2023