A289091 Decimal expansion of (E(|x|^5))^(1/5), with x being a normally distributed random variable.

1, 4, 4, 8, 7, 9, 1, 9, 0, 1, 5, 4, 9, 3, 0, 5, 2, 8, 5, 2, 5, 3, 5, 4, 6, 5, 9, 8, 8, 1, 2, 8, 1, 0, 5, 8, 8, 2, 1, 3, 4, 0, 1, 0, 3, 9, 3, 5, 1, 9, 6, 7, 8, 0, 7, 2, 9, 5, 0, 3, 0, 5, 8, 0, 1, 5, 5, 4, 3, 6, 2, 8, 4, 7, 7, 4, 2, 7, 2, 8, 1, 2, 0, 5, 4, 2, 7, 4, 0, 2, 8, 1, 2, 4, 3, 6, 3, 3, 8, 6, 9, 7, 4, 9, 6

Offset: 1

Author

Stanislav Sykora, Jul 26 2017

Keywords

• nonn
• cons

Comments

The 5th root r(5) of the expected value E(|x|^5) for a normal distribution with zero mean and standard deviation 1. See A289090 for more details.

Examples

			1.44879190154930528525354659881281058821340103935196780729503058015...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..1000
• Wikipedia, Normal distribution

Crossrefs

Cf. A060294, A076668 (p=1), A289090 (p=3), A011002 (p=4), A011350 (p=6).

Programs

PARI

// General code, for any p > 0:
r(p) = (sqrt(2/Pi)^(p%2)*prod(k=0,(p-2)\2,p-1-2*k))^(1/p);
a = r(5) // Present instance

Formula

a = r(5), where r(p) = ((p-1)!!*sqrt(2/Pi))^(1/p).

a = (8*A076668)^(1/5).