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%I #13 Nov 13 2014 03:22:57
%S 1,3,15,105,945,10263,127699,1751685,25807445,401449271,6519160851,
%T 109656966853,1899821492925,33757439931675,613135175204151,
%U 11352879180474205,213825919244349885,4089023317563827335,79269914519539177315,1555788699527063688453
%N Expected value of trace(O)^(2n), where O is a 5 X 5 orthogonal matrix randomly selected according to Haar measure.
%C The corresponding sequences for 2 X 2, 3 X 3, and 4 X 4 matrices are A001700, A099251, and A246860.
%C This sequence is a bisection of A095922. - _Nathaniel Johnston_, Nov 03 2014
%H MathOverflow, <a href="http://mathoverflow.net/questions/180110/moments-of-the-trace-of-orthogonal-matrices">Moments of the trace of orthogonal matrices</a>
%p A247304 := proc (n) return (1/2)*integrate(integrate((1-cos(x))*(1-cos(y))*(cos(x)-cos(y))^2*(1+2*cos(x)+2*cos(y))^(2*n), y = 0 .. 2*Pi), x = 0 .. 2*Pi)/Pi^2 end proc; seq(A247304(n), n = 1 .. 20);
%Y Cf. A001700, A095922, A099251, A246860, A247306.
%K nonn
%O 1,2
%A _Nathaniel Johnston_, Sep 11 2014
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