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 A272865 #18 Jul 20 2019 12:27:14
%S A272865 4,24,160,132,936,5700,720,5312,33264,198144,3940,29880,190980,
%T A272865 1155600,6823620,21672,167712,1088856,6670656,39786120,233908896,
%U A272865 119812,941640,6189540,38300976,230340740,1363667256,7997325700
%N A272865 Triangle read by rows, T(n,k) are covariances of inverse power traces of complex Wishart matrices with parameter c=2, for n>=1 and 1<=k<=n.
%C A272865 These numbers provide the covariances of power traces of the time-delay matrix when the scattering matrix belongs to the Dyson ensembles.
%C A272865 Relation with A047781 and A002002. See eq. (60) and (61) in Cunden et al., J. Phys. A: Math. Theor. 49, 18LT01 (2016).
%D A272865 F. D. Cunden, "Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities", Phys. Rev. E 91, 060102(R) (2015).
%D A272865 F. D. Cunden, F. Mezzadri, N. Simm and P. Vivo, "Correlators for the Wigner-Smith time-delay matrix of chaotic cavities", J. Phys. A: Math. Theor. 49, 18LT01 (2016).
%D A272865 F. D. Cunden, F. Mezzadri, N. O'Connell and N. Simm, "Moments of Random Matrices and Hypergeometric Orthogonal Polynomials", Commun. Math. Phys. 369, 1091-1145 (2019).
%H A272865 F. D. Cunden, <a href="http://arxiv.org/abs/1412.2172">Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities</a>, arXiv:1412.2172 [cond-mat.mes-hall], 2014-2015.
%H A272865 F. D. Cunden, F. Mezzadri, N. Simm and P. Vivo, <a href="http://arxiv.org/abs/1601.06690">Correlators for the Wigner-Smith time-delay matrix of chaotic cavities</a>, arXiv:1601.06690 [math-ph], 2016.
%H A272865 F. D. Cunden, F. Mezzadri, N. O'Connell and N. Simm, <a href="https://arxiv.org/abs/1805.08760">Moments of Random Matrices and Hypergeometric Orthogonal Polynomials</a>, arXiv:1805.08760 [math-ph], 2018.
%F A272865 G.f.: ((x*y)/(x-y)^2)*((x*y-3(x+y)+1)/(sqrt(x^2-6x+1)*sqrt(y^2-6y+1))-1).
%F A272865 T(n,1)/4 = A050151(n) for n>=1. - _Peter Luschny_, May 08 2016
%e A272865 Triangle starts:
%e A272865 4;
%e A272865 24, 160;
%e A272865 132, 936, 5700;
%e A272865 720, 5312, 33264, 198144;
%e A272865 3940, 29880, 190980, 1155600, 6823620;
%p A272865 P := (n,k) -> simplify(n*hypergeom([1-k,k+1],[1],-1)*hypergeom([1-n,n+1],[2],-1)): seq(seq(4*(n*k)*(P(n,k)+P(k,n))/(n+k),k=1..n),n=1..7); # _Peter Luschny_, May 08 2016
%t A272865 Clear["Global`*"];(*Wigner-Smith Covariance*)
%t A272865 P[k_] := Sum[Binomial[k - 1, j] Binomial[k + j, j], {j, 0, k - 1}]
%t A272865 Q[k_] := Sum[Binomial[k, j + 1] Binomial[k + j, j], {j, 0, k - 1}]
%t A272865 a[k1_, k2_] := 4 (k1 k2)/(k1 + k2) (P[k1] Q[k2] + P[k2] Q[k1])
%t A272865 L = 10; Table[a[k, l], {k, 1, L}, {l, 1, k}]
%Y A272865 Cf. A002002, A047781, A050151.
%K A272865 nonn,tabl
%O A272865 1,1
%A A272865 _Fabio Deelan Cunden_, May 08 2016