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a(n) = (n!!)^2 - n!.
0

%I #8 Oct 14 2016 11:31:22

%S 2,3,40,105,1584,5985,107136,530145,11116800,68139225,1644364800,

%T 12034447425,329001523200,2801155982625,85619242598400,

%U 831764543234625,28117244819865600,307025061241523625,11374945402060800000

%N a(n) = (n!!)^2 - n!.

%F E.g.f.: x*(1 - sqrt(1 - x^2) + arcsin(x))/(1 - x^2)^(3/2). - _Benedict W. J. Irwin_, Oct 14 2016

%t Table[CoefficientList[Series[(x(1-Sqrt[1-x^2]+ArcSin[x]))/(1-x^2)^(3/2), {x, 0, 20}], x][[n]](n-1)!, {n, 3, 20}] (* _Benedict W. J. Irwin_, Oct 14 2016 *)

%K nonn

%O 2,1

%A _Vladeta Jovovic_, Oct 31 2003