|
Search: id:A088505
|
|
|
| A088505 |
|
a(n)=(2^(3*n-1))/(integral_{x = 0 to 1} (1-x^4)^n dx). |
|
+0
1
|
|
| 5, 45, 390, 3315, 27846, 232050, 1922700, 15862275, 130423150, 1069469830, 8750207700, 71460029550, 582674087100, 4744631852100, 38589672397080, 313541088226275, 2545215892660350, 20644528907133950, 167329339563085700
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
FORMULA
|
The integral is equal to n!*Pi*sqrt(2)/(4*GAMMA(3/4)*GAMMA(n+5/4)). - njas
|
|
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}] (from Robert G. Wilson v Feb 26 2004)
|
|
PROGRAM
|
(PARI) a(n)=round(2^(3*n-1)/(n!*Pi*sqrt(2)/(4*gamma(3/4)*gamma(n+5/4))))
|
|
CROSSREFS
|
Adjacent sequences: A088502 A088503 A088504 this_sequence A088506 A088507 A088508
Sequence in context: A043025 A125836 A001260 this_sequence A067403 A022022 A058410
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Al Hakanson (hawkuu(AT)excite.com), Nov 13 2003
|
|
EXTENSIONS
|
More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 14 2003
|
|
|
Search completed in 0.002 seconds
|
