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%I #12 Dec 16 2016 02:40:38
%S 1,1,1,1,3,1,1,3,10,1,1,3,15,35,1,1,3,15,91,126,1,1,3,15,105,603,462,
%T 1,1,3,15,105,903,4213,1716,1,1,3,15,105,945,8778,30537,6435,1,1,3,15,
%U 105,945,10263,92235,227475,24310,1
%N Array T(n,k) of the expected value of trace(O)^(2k), where O is an n X n orthogonal matrix randomly selected according to Haar measure, read by antidiagonals.
%C The expected value of trace(O)^k, when k is an odd natural number, is zero.
%C The first 5 rows of this array are A000012, A001700, A099251, A246860, and A247304.
%C T(n,k) = A001147(k) when k <= n. When k > n, T(n,k) < A001147(k).
%H L. Pastur and V. Vasilchuk, <a href="http://www-old.newton.ac.uk/preprints/NI04015.pdf">On the moments of traces of matrices of classical groups</a>, Commun. Math. Phys. 252:149-166, 2004.
%H MathOverflow, <a href="http://mathoverflow.net/questions/180110/moments-of-the-trace-of-orthogonal-matrices">Moments of the trace of orthogonal matrices</a>.
%e The upper-left corner of the array begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 3, 10, 35, 126, 462, 1716, ...
%e 1, 3, 15, 91, 603, 4213, 30537, ...
%e 1, 3, 15, 105, 903, 8778, 92235, ...
%e 1, 3, 15, 105, 945, 10263, 127699, ...
%Y Cf. A001147, A001700, A099251, A246860, and A247304.
%K nonn,tabl
%O 1,5
%A _Nathaniel Johnston_, Sep 11 2014
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