A088505 a(n) = (2^(3*n-1))/(integral_{x=0..1} (1-x^4)^n dx).

5, 45, 390, 3315, 27846, 232050, 1922700, 15862275, 130423150, 1069469830, 8750207700, 71460029550, 582674087100, 4744631852100, 38589672397080, 313541088226275, 2545215892660350, 20644528907133950, 167329339563085700

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Formula

The integral is equal to n!*Pi*sqrt(2)/(4*GAMMA(3/4)*GAMMA(n+5/4)). - N. J. A. Sloane

GAMMA(3/4)*GAMMA(n+5/4) is Pi*sqrt(2)*A007696(n+1)/4^(n+1), so the integral is n!*4^n/A007695(n+1) and a(n) = 2^(n-1)*A007696(n+1)/n!. - R. J. Mathar, Feb 04 2021

D-finite with recurrence n*a(n) +2*(-4*n-1)*a(n-1)=0. - R. J. Mathar, Feb 04 2021

Example

a(3)=390 (a(0) would be 1/2, so the sequence begins at n=1).

Mathematica

f[n_] := 2^(3n - 1)/Integrate[(1 - x^4)^n, {x, 0, 1}]; Table[ f[n], {n, 1, 19}] (* Robert G. Wilson v, Feb 26 2004 *)

Prog

(PARI) a(n)=round(2^(3*n-1)/(n!*Pi*sqrt(2)/(4*gamma(3/4)*gamma(n+5/4))))

Crossrefs

Sequence in context: A185009 A125836 A001260 * A067403 A173292 A173558

Adjacent sequences: A088502 A088503 A088504 * A088506 A088507 A088508

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)excite.com), Nov 13 2003

Extensions

More terms from Benoit Cloitre, Nov 14 2003

Status

approved