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Denominator of (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).
3

%I #13 Apr 12 2017 16:06:43

%S 1,6,24,432,10368,6912,248832,1492992,23887872,1289945088,15479341056,

%T 30958682112,2229025112064,13374150672384,5944066965504,

%U 106993205379072,10271347716390912,20542695432781824,2218611106740436992,13311666640442621952,106493333123540975616

%N Denominator of (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).

%F A285019(n)/a(n) = (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).

%F Sum_{k>=0} A285019(k)/a(k) = sqrt(3/2).

%F Sum_{k>=0} (-1)^k*A285019(k)/a(k) = sqrt(3)/2.

%F Sum_{k>=0} (-1)^(k+1)*A285019(k)/a(k) = -sqrt(3)/2.

%p P:=proc(q) denom((-1/3)^q*sqrt(Pi)/(GAMMA(1/2-q)*GAMMA(1+q))); end:

%p seq(P(i),i=0..20); # _Paolo P. Lava_, Apr 10 2017

%t Denominator[Table[(-1/3)^n*Sqrt[Pi]/(Gamma[1/2-n]*Gamma[1+n]),{n,0,25}]]

%Y Cf. A285019 (numerators).

%K nonn,frac

%O 0,2

%A _Ralf Steiner_, Apr 08 2017