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A145921 Numerator of n*B(n,1+1/n), where B(.,.) is the Beta Function. 1
1, 8, 81, 2048, 15625, 6718464, 5764801, 2147483648, 31381059609, 64000000000000, 3138428376721, 2218611106740436992, 3937376385699289, 1115112108958398021632, 39903080760955810546875 (list; graph; refs; listen; history; text; 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.

LINKS

Table of n, a(n) for n=1..15.

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) ;

MATHEMATICA

Table[Numerator[n Beta[n, 1 + 1/n]], {n, 1, 15}] (* Jean-Fran├žois Alcover, Sep 26 2018 *)

PROG

(DERIVE) VECTOR(NUMERATOR(F(n)), n, 1, 10)

CROSSREFS

Sequence in context: A193563 A026845 A305770 * A304655 A100399 A022504

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, Dec 08 2008

STATUS

approved

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Last modified August 8 02:22 EDT 2020. Contains 336290 sequences. (Running on oeis4.)