A285018 Denominator of (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).

1, 6, 24, 432, 10368, 6912, 248832, 1492992, 23887872, 1289945088, 15479341056, 30958682112, 2229025112064, 13374150672384, 5944066965504, 106993205379072, 10271347716390912, 20542695432781824, 2218611106740436992, 13311666640442621952, 106493333123540975616

Offset: 0

Author

Ralf Steiner, Apr 08 2017

Keywords

• nonn
• frac

Crossrefs

Cf. A285019 (numerators).

Programs

Maple

P:=proc(q) denom((-1/3)^q*sqrt(Pi)/(GAMMA(1/2-q)*GAMMA(1+q))); end:
seq(P(i),i=0..20); # Paolo P. Lava, Apr 10 2017

Mathematica

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

Formula

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

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

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

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