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A285019
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Numerator of (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).
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3
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1, 1, 1, 5, 35, 7, 77, 143, 715, 12155, 46189, 29393, 676039, 1300075, 185725, 1077205, 33393355, 21607465, 756261275, 1472719325, 3829070245, 22427411435, 87670790155, 19058867425, 895766768975, 1755702867191
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n)/A285018(n) = (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).
Sum_{k>=0} a(k)/A285018(k) = sqrt(3/2).
Sum_{k>=0} (-1)^k*a(k)/A285018(k) = sqrt(3)/2.
Sum_{k>=0} (-1)^(k+1)*a(k)/A285018(k) = -sqrt(3)/2.
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MAPLE
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P:=proc(q) numer((-1/3)^q*sqrt(Pi)/(GAMMA(1/2-q)*GAMMA(1+q))); end:
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MATHEMATICA
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Numerator[Table[(-1/3)^n*Sqrt[Pi]/(Gamma[1/2-n]*Gamma[1+n]), {n, 0, 25}]]
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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