A146753 a(n) = denominator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).

1, 10, 110, 1870, 8602, 249458, 1247290, 51138890, 218502530, 2316126818, 136651482262, 136651482262, 570720896506, 6277929861566, 521068178509978, 46375067887388042, 2016307299451654, 203647037244617054

Offset

0,2

Comments

Previous name was: a(n)=denominator of k_n such that Integrate[(1+x^(3n))/Sqrt[1-x^3],{x,0,1}]= k_n*(Gamma[1/3]^3)/(2^(1/3)Sqrt[3]Pi) where n >= 0.

General formula: Integral_{x=0..1} ((1+x^(3n))/sqrt(1-x^3)) dx = G_3 * k_n = G_3*A146752(n)/A146753(n) = A118292*A146752(n)/A146753(n) where G_3 = (Gamma(1/3)^3)/(2^(1/3)*sqrt(3)*Pi).

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = denominator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).

Mathematica

Table[Denominator[(1/2) (1 + Product[(2 (1 + 3 k))/(5 + 6 k), {k, 0, n - 1}])], {n, 0, 30}]

Crossrefs

Cf. A146752 (numerator), A118292 (G_3).

Sequence in context: A108487 A099883 A337351 * A297500 A305213 A181929

Adjacent sequences: A146750 A146751 A146752 * A146754 A146755 A146756

Keyword

nonn,frac

Author

Artur Jasinski, Nov 01 2008

Extensions

New name (using given formula) from Joerg Arndt, Sep 24 2022

Status

approved