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 A089272 #12 Jul 02 2023 18:23:33
%S A089272 1,48,1412,34400,766416,16296448,337709632,6896540160,139644851456,
%T A089272 2813500878848,56517475402752,1133320271749120,22702062218039296,
%U A089272 454469171469877248,9094518828981174272,181952003020274401280
%N A089272 Fourth column (k=5) of array A078739(n,k) ((2,2)- generalized Stirling2) divided by 12.
%C A089272 The numerator of the g.f. is the n=2 row polynomial of the triangle A089276.
%D A089272 P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003), 198-205.
%H A089272 P. Blasiak, K. A. Penson and A. I. Solomon, <a href="https://arxiv.org/abs/quant-ph/0402027">The general boson normal ordering problem</a>, arXiv:quant-ph/0402027, 2004.
%H A089272 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (40, -508, 2304, -2880).
%F A089272 G.f. (1+8*x)/((1-2*1*x)*(1-3*2*x)*(1-4*3*x)*(1-5*4*x)).
%F A089272 a(n)= (3500*20^n - 3780*12^n + 945*6^n - 35*2^n)/630 = d(n) + 8*d(n-1), with d(n) := A071952(n+4)= (2500*20^n - 2268*12^n + 405*6^n - 7*2^n)/630, n>=1.
%t A089272 LinearRecurrence[{40, -508, 2304, -2880}, {1, 48, 1412, 34400}, 16] (* _Jean-François Alcover_, Feb 28 2020 *) (* _Jean-François Alcover_, Feb 28 2020 *)
%Y A089272 Cf. A071952, A089271, A089273, A071951 (Legendre-Stirling triangle).
%K A089272 nonn,easy
%O A089272 0,2
%A A089272 _Wolfdieter Lang_, Nov 07 2003