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

%I A289091 #11 Jul 27 2017 14:13:40
%S A289091 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,
%T A289091 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,
%U A289091 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
%N A289091 Decimal expansion of (E(|x|^5))^(1/5), with x being a normally distributed random variable.
%C A289091 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.
%H A289091 Stanislav Sykora, <a href="/A289091/b289091.txt">Table of n, a(n) for n = 1..1000</a>
%H A289091 Wikipedia, <a href="https://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
%F A289091 a = r(5), where r(p) = ((p-1)!!*sqrt(2/Pi))^(1/p).
%F A289091 a = (8*A076668)^(1/5).
%e A289091 1.44879190154930528525354659881281058821340103935196780729503058015...
%o A289091 (PARI) // General code, for any p > 0:
%o A289091 r(p) = (sqrt(2/Pi)^(p%2)*prod(k=0,(p-2)\2,p-1-2*k))^(1/p);
%o A289091 a = r(5) // Present instance
%Y A289091 Cf. A060294, A076668 (p=1), A289090 (p=3), A011002 (p=4), A011350 (p=6).
%K A289091 nonn,cons
%O A289091 1,2
%A A289091 _Stanislav Sykora_, Jul 26 2017