OFFSET
0,2
EXAMPLE
MAPLE
a:= n-> numer(sqrt(2)*int(1/(1-x^2)^(n+3/2), x=0..sqrt(1/3))):
seq(a(n), n=0..20); # Alois P. Heinz, Mar 29 2015
MATHEMATICA
f[n_] := Numerator[ Simplify[ Sqrt[2]*Integrate[1/(1 - x^2)^(n + 1/2), {x, 0, Sqrt[1/3]}]]]; Table[ f[n], {n, 1, 20}] (* Robert G. Wilson v, Feb 27 2004 *)
Numerator[Table[Sqrt[2/3] * Hypergeometric2F1[1/2, n+3/2, 3/2, 1/3], {n, 0, 20}]] (* Vaclav Kotesovec, Apr 08 2015 *)
a[n_] := Hypergeometric2F1[-n, 1/2, 3/2, -1/2]
Table[Numerator[a[n]], {n, 0, 20}] (* Gerry Martens, Aug 09 2015 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Al Hakanson (hawkuu(AT)excite.com), Dec 26 2003
EXTENSIONS
More terms from Robert G. Wilson v, Feb 27 2004
STATUS
approved