A089342 Numerator of sqrt(2) * Integral_{x=0..sqrt(1/3)} 1/(1-x^2)^(n+3/2) dx.

1, 7, 83, 467, 10307, 56537, 620695, 3421003, 151692131, 846015389, 1356505339, 7657542115, 173845651297, 991488244363, 79507898457503, 457142023114427, 42194359402773923, 244118009518249157, 2831917415062783681, 16462724429712384049, 383563872480791378989

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Example

1/1, 7/6, 83/60, 467/280, 10307/5040, 56537/22176, 620695/192192, 3421003/823680, 151692131/28005120, 846015389/118243840, 1356505339/141892608, ... = A089342/A256442.

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

Denominators are in A256442.

Sequence in context: A304591 A139951 A141872 * A297716 A075137 A268704

Adjacent sequences: A089339 A089340 A089341 * A089343 A089344 A089345

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