|
| |
|
|
A145921
|
|
Numerator of n*B(n,1+1/n), where B(.,.) is the Beta Function.
|
|
0
| |
|
|
1, 8, 81, 2048, 15625, 6718464, 5764801, 2147483648, 31381059609, 64000000000000, 3138428376721, 2218611106740436992, 3937376385699289, 1115112108958398021632, 39903080760955810546875
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| n*B(n,1+1/n) = Gamma(n+1)*Gamma(1+1/n)/Gamma(1+n+1/n) is the integral over F(n)=[1-x^(1/n)]^(1/n) from x=0 to 1.
|
|
|
EXAMPLE
| The fractions are 1/2, 8/15, 81/140, 2048/3315, 15625/24024, ...
|
|
|
MAPLE
| seq( numer(n*Beta(n, 1+1/n)), n=1..30) ;
|
|
|
PROG
| (DERIVE) VECTOR(NUMERATOR(F(n)), n, 1, 10)
|
|
|
CROSSREFS
| Sequence in context: A138439 A193563 A026845 * A100399 A022504 A104126
Adjacent sequences: A145918 A145919 A145920 * A145922 A145923 A145924
|
|
|
KEYWORD
| nonn,frac
|
|
|
AUTHOR
| Jose Luis (jl_altamirano(AT)yahoo.com), Oct 25 2008
|
|
|
EXTENSIONS
| Definition clarified by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2008
|
| |
|
|
