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Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*i-1)!,i=1..n).
0

%I #7 Nov 21 2013 12:45:53

%S 0,2,-20,894,-76936,11218330,-2486192988,779417002070,

%T -328459055125136,179127562413460914,-122758432482044667940,

%U 103274000340320165525422,-104642430930574639703548440,125699390463431456337149276234

%N Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*i-1)!,i=1..n).

%t Table[Sum[(-1)^(i+1) Binomial[n,i]2^i (2i-1)!,{i,n}],{n,0,20}] (* _Harvey P. Dale_, Oct 13 2011 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_.