A090598 Numerator of ((integral_{x = 0..1/2} 1/(1+x^2)^(n + 1/2) dx) * sqrt(1/5)).

1, 14, 328, 10800, 458880, 23911680, 1477278720, 105623562240, 8582728089600, 781478859571200, 78834419151667200, 8729454895025356800, 1052840115930503577600, 137399767923711541248000

Offset

1,2

Comments

Denominator is b(n)=5^(n-1)*(2*n)!/(n!*2^n). E.g., b(3)=375.

Links

Table of n, a(n) for n=1..14.

Example

a(3) = 328 since f(n) = 328/375.

Mathematica

f[n_] := (5^(n - 1/2)(2n - 1)!!Integrate[1/(1 + x^2)^(n + 1/2), {x, 0, 1/2}]); Table[ f[n], {n, 1, 15}] (* Robert G. Wilson v, Feb 27 2004 *)

Crossrefs

Sequence in context: A275397 A275262 A241373 * A277769 A060075 A222984

Adjacent sequences: A090595 A090596 A090597 * A090599 A090600 A090601

Keyword

nonn,frac

Author

Al Hakanson (hawkuu(AT)excite.com), Feb 25 2004

Extensions

Edited and extended by Robert G. Wilson v, Feb 27 2004

Status

approved