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 A370953 #26 May 02 2024 17:05:39
%S A370953 1,1,4,77,1009,101627,1302779,2513121979,11291682179,1354947005798,
%T A370953 23064317580681848,20189102649892270054,776220757551441546419,
%U A370953 641273428219629914673014,5433381672262390009892530636,1399751922597075578762073697769
%N A370953 Numerators of coefficients of the partition function per spin, lambda (divided by 2), in the very high temperature region, expressed as a power series in the parameter K^2, for the spin-1/2 Ising model on square lattice.
%H A370953 Hendrik A. Kramers and Gregory H. Wannier. <a href="https://doi.org/10.1103/PhysRev.60.252">Statistics of the two-dimensional ferromagnet. Part I</a>. Phys. Rev. 60 (1941), 252-262.
%H A370953 Hendrik A. Kramers and Gregory H. Wannier. <a href="https://doi.org/10.1103/PhysRev.60.263">Statistics of the two-dimensional ferromagnet. Part II</a>. Phys. Rev. 60 (1941), 263-276. See (41), p. 263.
%H A370953 Hendrik A. Kramers and Gregory H. Wannier, <a href="/A370953/a370953.pdf">Extract from page 263 of Part II.</a>
%H A370953 Gandhimohan M. Viswanathan, <a href="https://doi.org/10.1088/1742-5468/2015/07/P07004">The hypergeometric series for the partition function of the 2D Ising model</a>, J. Stat. Mech. (2015) P07004; arXiv:<a href="https://arxiv.org/abs/1411.2495">1411.2495</a> [cond-mat.stat-mech], 2014-2015.
%H A370953 Wikipedia, <a href="https://en.wikipedia.org/wiki/Square_lattice_Ising_model">Square lattice Ising model</a>.
%F A370953 a(n) / A370954(n) ~ c * 2^(2*n) / (n^3 * log(1 + sqrt(2))^(2*n)), where c = 0.15662885... - _Vaclav Kotesovec_, May 02 2024
%t A370953 CoefficientList[With[{nmax = 7}, Exp[-Log[2]/2 + 1/(2 Pi) Integrate[Log[Cosh[2k]^2 + Sqrt[Sinh[2k]^4 + 1 - 2 Sinh[2k]^2 Cos[2\[Theta]] + O[k]^(2nmax+1)]], {\[Theta], 0, Pi}] + O[k]^(2nmax+1)]], k][[;; ;; 2]] // Numerator (* _Andrey Zabolotskiy_, Mar 10 2024 *)
%t A370953 CoefficientList[Cosh[2k] Exp[-x HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 2}, 16x] /. {x -> (Sinh[2k]/(2Cosh[2k]^2))^2}] + O[k]^32, k][[;; ;; 2]] // Numerator (* _Andrey Zabolotskiy_, Mar 13 2024, using the g. f. from Gandhimohan M. Viswanathan *)
%Y A370953 See A370954 for denominators.
%Y A370953 Cf. A370955, A002908, A002890.
%K A370953 nonn,frac
%O A370953 0,3
%A A370953 _N. J. A. Sloane_, Mar 10 2024
%E A370953 Terms a(5) and beyond from _Andrey Zabolotskiy_, Mar 10 2024