n | 1 | 2 | 3 | 4 | 5 C_n | 1 | 2 | 5 | 14 | 42

(2^(2 n) Γ(n + 1/2))/(sqrt(π) Γ(n + 2))

n = -2

n = -3

n = -4

n = -5

n = -6

n = -7

n = -8

n = -9

1 - n + 1/6 (6 + π^2) n^2 + n^3 (-2 ζ(3) - 1 - π^2/6) + n^4 (2 ζ(3) + 1 + π^2/6 + (19 π^4)/360) + O(n^5) (Taylor series)

4^n ((1/n)^(3/2)/sqrt(π) - (9 (1/n)^(5/2))/(8 sqrt(π)) + (145 (1/n)^(7/2))/(128 sqrt(π)) - (1155 (1/n)^(9/2))/(1024 sqrt(π)) + O((1/n)^(11/2)))

d/dn(C_n) = C_n (polygamma(0, n + 1/2) - polygamma(0, n + 2) + log(4))

C_n = binomial(2 n, n)/(1 + n)

C_n = 1/(n (1 + n) beta(n, 1 + n))

C_n = (1 + n)_n/Γ(2 + n)

C_n ∝(4^n sum_(k=0)^∞ ((-1)^k n^(-k) B_k^(-1/2)(1/2) (3/2)_k)/(k!))/(n^(3/2) sqrt(π)) for (abs(arg(1/2 + n))<π and abs(n)->∞)

C_n ∝(4^n sqrt(-n) ( sum_(k=0)^∞ ((-1)^k n^(-k) B_k^(-1/2)(1/2) (3/2)_k)/(k!)) tan(n π))/(n^2 sqrt(π)) for (arg(n) = π and 1/2 + n not element Z and abs(n)->∞)

C_n ∝(2^(2 n) ( sum_(k=0)^∞ ((-1)^k n^(-k) B_k^(-1/2)(1/2) (3/2)_k)/(k!)) ((n^(3/2) tan(n π))/(-n)^(3/2))^floor((π + arg(n))/(2 π)))/(n^(3/2) sqrt(π)) for ((1/2 - n not element Z or 2 n>=1) and abs(n)->∞)