|
|
A146752
|
|
a(n) = numerator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).
|
|
3
|
|
|
1, 7, 71, 1159, 5197, 148025, 730141, 29616293, 125438657, 1319937329, 77390680651, 76972298827, 319946679037, 3504590799071, 289784158718029, 25703039917515461, 1114069690728835, 112203290640603311
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
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).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = numerator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).
|
|
MATHEMATICA
|
Table[Numerator[(1/2) (1 + Product[(2 (1 + 3 k))/(5 + 6 k), {k, 0, n - 1}])], {n, 0, 30}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Simpler name (using given formula) from Joerg Arndt, Sep 24 2022
|
|
STATUS
|
approved
|
|
|
|