A146752 a(n) = numerator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).

1, 7, 71, 1159, 5197, 148025, 730141, 29616293, 125438657, 1319937329, 77390680651, 76972298827, 319946679037, 3504590799071, 289784158718029, 25703039917515461, 1114069690728835, 112203290640603311

Offset: 0

Author

Artur Jasinski, Nov 01 2008

Keywords

• nonn
• frac

Comments

Previous name was: a(n) is the numerator of k_n such that Integral_{x=0..1} ((1+x^(3n))/sqrt(1-x^3)) dx = k_n*Gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi) for 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).

Crossrefs

Cf. A146753 (denominator), A118292 (G_3).

Programs

Mathematica

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

Formula

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

Extensions

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