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A088505 a(n) = (2^(3*n-1))/(integral_{x=0..1} (1-x^4)^n dx). 0
5, 45, 390, 3315, 27846, 232050, 1922700, 15862275, 130423150, 1069469830, 8750207700, 71460029550, 582674087100, 4744631852100, 38589672397080, 313541088226275, 2545215892660350, 20644528907133950, 167329339563085700 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified July 18 15:26 EDT 2019. Contains 325143 sequences. (Running on oeis4.)