# 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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC