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 A089271 #23 Oct 22 2024 14:34:23
%S A089271 1,38,652,9080,116656,1446368,17636032,213311360,2569812736,
%T A089271 30898216448,371141389312,4455873443840,53483541999616,
%U A089271 641880868118528,7703040602324992,92439308337643520,1109288626710839296
%N A089271 Third column (k=4) of array A078739(n,k) ((2,2)-generalized Stirling2).
%C A089271 The numerator of the g.f. is the n=2 row polynomial of the triangle A089275.
%H A089271 Vincenzo Librandi, <a href="/A089271/b089271.txt">Table of n, a(n) for n = 0..500</a>
%H A089271 P. Blasiak, K. A. Penson and A. I. Solomon, <a href="http://dx.doi.org/10.1016/S0375-9601(03)00194-4">The general boson normal ordering problem</a>, Phys. Lett. A 309 (2003) 198-205.
%H A089271 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 A089271 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20, -108, 144).
%F A089271 G.f.: (1+18*x)/((1-2*1*x)*(1-3*2*x)*(1-4*3*x)).
%F A089271 a(n) = 6*12^n - 6*6^n + 2^n = d(n) + 18*d(n-1), n>=1, a(0)=1, with d(n) := A016309(n) = A071951(n+3, 3) = (24*12^n-15*6^n+2^n)/10.
%t A089271 Table[6*12^n -6*6^n +2^n, {n,0,30}] (* _G. C. Greubel_, Feb 07 2018 *)
%t A089271 LinearRecurrence[{20,-108,144},{1,38,652},20] (* _Harvey P. Dale_, Oct 22 2024 *)
%o A089271 (Magma) [6*12^n-6*6^n+2^n: n in [0..20]]; // _Vincenzo Librandi_, Sep 02 2011
%o A089271 (PARI) for(n=0,30, print1(6*12^n -6*6^n +2^n, ", ")) \\ _G. C. Greubel_, Feb 07 2018
%Y A089271 Cf. A089272, A071951 (Legendre-Stirling triangle).
%K A089271 nonn,easy
%O A089271 0,2
%A A089271 _Wolfdieter Lang_, Nov 07 2003