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 A247304 Expected value of trace(O)^(2n), where O is a 5 X 5 orthogonal matrix randomly selected according to Haar measure. 5
 1, 3, 15, 105, 945, 10263, 127699, 1751685, 25807445, 401449271, 6519160851, 109656966853, 1899821492925, 33757439931675, 613135175204151, 11352879180474205, 213825919244349885, 4089023317563827335, 79269914519539177315, 1555788699527063688453 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The corresponding sequences for 2 X 2, 3 X 3, and 4 X 4 matrices are A001700, A099251, and A246860. This sequence is a bisection of A095922. - Nathaniel Johnston, Nov 03 2014 LINKS MathOverflow, Moments of the trace of orthogonal matrices MAPLE 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); CROSSREFS Cf. A001700, A095922, A099251, A246860, A247306. Sequence in context: A295871 A293997 A328866 * A293998 A293999 A294000 Adjacent sequences:  A247301 A247302 A247303 * A247305 A247306 A247307 KEYWORD nonn AUTHOR Nathaniel Johnston, Sep 11 2014 STATUS approved

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)