A285019 - OEIS

A285019

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

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

0,4

LINKS

Table of n, a(n) for n=0..25.

FORMULA

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.

MAPLE

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

seq(P(i), i=0..25); # Paolo P. Lava, Apr 10 2017

MATHEMATICA

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

CROSSREFS

Cf. A285018 (denominators).

Sequence in context: A216759 A144995 A173865 * A169617 A174130 A095865

Adjacent sequences: A285016 A285017 A285018 * A285020 A285021 A285022

KEYWORD

nonn,frac

AUTHOR

Ralf Steiner, Apr 08 2017

STATUS

approved