A145921 Numerator of n*B(n,1+1/n), where B(.,.) is the Beta Function.

1, 8, 81, 2048, 15625, 6718464, 5764801, 2147483648, 31381059609, 64000000000000, 3138428376721, 2218611106740436992, 3937376385699289, 1115112108958398021632, 39903080760955810546875, 604462909807314587353088, 14063084452067724991009, 16918235275724100929608539439104

Offset: 1

Author

Jose Luis (jl_altamirano(AT)yahoo.com), Oct 25 2008

Keywords

• nonn
• frac

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.

Examples

			The fractions are 1/2, 8/15, 81/140, 2048/3315, 15625/24024, ...
		

Programs

Derive

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

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-François Alcover, Sep 26 2018 *)

Extensions

Definition clarified by R. J. Mathar, Dec 08 2008