Fungrim entry: 37fb5f

G = \frac{1}{64} \sum_{n=1}^{\infty} \frac{{256}^{n} \left(580 {n}^{2} - 184 n + 15\right)}{{n}^{3} \left(2 n - 1\right) {6 n \choose 3 n} {6 n \choose 4 n} {4 n \choose 2 n}}

References:

https://hal.inria.fr/hal-00990465/

TeX:

G = \frac{1}{64} \sum_{n=1}^{\infty} \frac{{256}^{n} \left(580 {n}^{2} - 184 n + 15\right)}{{n}^{3} \left(2 n - 1\right) {6 n \choose 3 n} {6 n \choose 4 n} {4 n \choose 2 n}}

Definitions:

Fungrim symbol	Notation	Short description
`ConstCatalan`	$G$	Catalan's constant
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power
`Binomial`	${n \choose k}$	Binomial coefficient
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("37fb5f"),
    Formula(Equal(ConstCatalan, Mul(Div(1, 64), Sum(Div(Mul(Pow(256, n), Add(Sub(Mul(580, Pow(n, 2)), Mul(184, n)), 15)), Mul(Mul(Mul(Mul(Pow(n, 3), Sub(Mul(2, n), 1)), Binomial(Mul(6, n), Mul(3, n))), Binomial(Mul(6, n), Mul(4, n))), Binomial(Mul(4, n), Mul(2, n)))), For(n, 1, Infinity))))),
    References("https://hal.inria.fr/hal-00990465/"))

Topics using this entry

Catalan's constant