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 A055856 #29 Jan 05 2025 02:09:19
%S A055856 1,16,90,328,888,2016,3994,7212,12070,19112,28846,41976,59116,81132,
%T A055856 108738,142972,184638,234952,294806,365596,448296,544492,655230,
%U A055856 782292,926794,1090716,1275238,1482548,1713880,1971636,2257102,2572896,2920350,3302308,3720138
%N A055856 Susceptibility series H_4 for 2-dimensional Ising model (divided by 2).
%H A055856 Colin Barker, <a href="/A055856/b055856.txt">Table of n, a(n) for n = 0..1000</a>
%H A055856 A. J. Guttmann and I. G. Enting, <a href="https://doi.org/10.1103/PhysRevLett.76.344">Solvability of some statistical mechanical systems</a>, Phys. Rev. Lett., 76 (1996), 344-347.
%H A055856 A. J. Guttmann, <a href="https://doi.org/10.1016/S0012-365X(99)00262-9">Indicators of solvability for lattice models</a>, Discrete Math., 217 (2000), 167-189.
%H A055856 D. Hansel et al., <a href="http://dx.doi.org/10.1007/BF01010400">Analytical properties of the anisotropic cubic Ising model</a>, J. Stat. Phys., 48 (1987), 69-80.
%H A055856 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-2,-4,0,4,2,-3,-1,1).
%F A055856 G.f.: (1 + 15*x + 71*x^2 + 192*x^3 + 326*x^4 + 388*x^5 + 326*x^6 + 192*x^7 + 71*x^8 + 15*x^9 + x^10)/((1-x^3)*(1-x)^4*(1+x)^3).
%F A055856 a(n) = (4794*n^4 + 19194*n^2 + 3349 - 81*(-1)^n*(2*n^2 + 5) + 512*ChebyshevT(n, -1/2))/1728, for n >= 1, with a(0) = 1. - _G. C. Greubel_, Jan 16 2020
%p A055856 1,seq( simplify( (4794*n^4 +19194*n^2 +3349 -81*(-1)^n*(2*n^2 +5) + 512*ChebyshevT(n, -1/2))/1728 ), n=1..40); # _G. C. Greubel_, Jan 16 2020
%t A055856 Join[{1}, Table[(4794*n^4 +19194*n^2 +3349 -81*(-1)^n*(2*n^2 +5) + 512*ChebyshevT[n, -1/2])/1728, {n,40}]] (* _G. C. Greubel_, Jan 16 2020 *)
%t A055856 LinearRecurrence[{1,3,-2,-4,0,4,2,-3,-1,1},{1,16,90,328,888,2016,3994,7212,12070,19112,28846},40] (* _Harvey P. Dale_, Jul 24 2021 *)
%o A055856 (PARI) Vec((1 +15*x +71*x^2 +192*x^3 +326*x^4 +388*x^5 +326*x^6 +192*x^7 + 71*x^8 +15*x^9 +x^10)/((1-x^3)*(1-x)^4*(1+x)^3) + O(x^40)) \\ _Colin Barker_, Dec 10 2016
%o A055856 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1 +15*x +71*x^2 +192*x^3 +326*x^4 +388*x^5 +326*x^6 +192*x^7 + 71*x^8 +15*x^9 +x^10)/((1-x^3)*(1-x^2)^3*(1-x)) )); // _G. C. Greubel_, Jan 16 2020
%o A055856 (Sage) [1]+[(4794*n^4 +19194*n^2 +3349 -81*(-1)^n*(2*n^2 +5) + 512*chebyshev_T(n, -1/2))/1728 for n in (1..40)] # _G. C. Greubel_, Jan 16 2020
%Y A055856 Cf. A054275, A054410, A054389, A054764, A055857.
%K A055856 nonn,easy
%O A055856 0,2
%A A055856 _Wolfdieter Lang_, Jun 07 2000