This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A247306 #12 Dec 16 2016 02:40:38 %S A247306 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 A247306 1,1,3,15,105,903,4213,1716,1,1,3,15,105,945,8778,30537,6435,1,1,3,15, %U A247306 105,945,10263,92235,227475,24310,1 %N A247306 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 A247306 The expected value of trace(O)^k, when k is an odd natural number, is zero. %C A247306 The first 5 rows of this array are A000012, A001700, A099251, A246860, and A247304. %C A247306 T(n,k) = A001147(k) when k <= n. When k > n, T(n,k) < A001147(k). %H A247306 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 A247306 MathOverflow, <a href="http://mathoverflow.net/questions/180110/moments-of-the-trace-of-orthogonal-matrices">Moments of the trace of orthogonal matrices</a>. %e A247306 The upper-left corner of the array begins: %e A247306 1, 1, 1, 1, 1, 1, 1, ... %e A247306 1, 3, 10, 35, 126, 462, 1716, ... %e A247306 1, 3, 15, 91, 603, 4213, 30537, ... %e A247306 1, 3, 15, 105, 903, 8778, 92235, ... %e A247306 1, 3, 15, 105, 945, 10263, 127699, ... %Y A247306 Cf. A001147, A001700, A099251, A246860, and A247304. %K A247306 nonn,tabl %O A247306 1,5 %A A247306 _Nathaniel Johnston_, Sep 11 2014