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Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*n-1)!,i=1..n) for n odd.
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%I #9 Oct 08 2023 18:01:00

%S 2,240,725760,12454041600,711374856192000,102181884343418880000,

%T 31022420086661971968000000,17683523987479403909087232000000,

%U 17366635237623772991036388802560000000,27527506182452690092631959163161804800000000

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

%F a(n) = 2*(4*n-3)!. - _Christian Krause_, Oct 08 2023

%o (PARI) a(n) = n=2*n-1; sum(i=1, n, (-1)^(i+1)*binomial(n,i)*2^i*(2*n-1)!); \\ _Michel Marcus_, Oct 08 2023

%Y Cf. A000142.

%K nonn

%O 1,1

%A _N. J. A. Sloane_.