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 A366672 #14 Nov 02 2023 04:57:34
%S A366672 1,2,49,39304,1908029761,8831763846882976,5602661527604399327549089,
%T A366672 659308109505417338723017914068713088,
%U A366672 18666765602783048904120522995911258148623099215361,159740893387079678500933964995221201596055121928224632284394525184
%N A366672 a(n) = A002720(n)^n.
%C A366672 This is the model count of the following sentence in first-order logic:
%C A366672 (forall w, x, y, z. P(x, y, z) /\ P(w, y, z) => x = w) /\
%C A366672 (forall w, x, y, z. P(x, y, z) /\ P(x, w, z) => y = w).
%H A366672 Paulius Dilkas and Vaishak Belle, <a href="https://arxiv.org/abs/2306.04189">Synthesising Recursive Functions for First-Order Model Counting: Challenges, Progress, and Conjectures</a>, KR 2023, 198-207; arXiv:2306.04189 [cs.LO], 2023.
%F A366672 a(n) ~ n^(n*(n + 1/4)) / (2^(n/2) * exp(n^2 - 2*n^(3/2) + n/2 - 31*sqrt(n)/48 + 17/192)) * (1 - 281/(5120*sqrt(n)) + 3074161/(52428800*n)). - _Vaclav Kotesovec_, Oct 20 2023
%e A366672 When n = 2, i.e., the domain is [2] = {1, 2}, both P(x, y, 1) and P(x, y, 2) represent partial injective functions from [2] to [2]. Since there are seven such functions, a(n) = 7^2 = 49.
%t A366672 Table[(n!*LaguerreL[n, -1])^n, {n, 0, 10}] (* _Vaclav Kotesovec_, Oct 20 2023 *)
%Y A366672 Cf. A002720, A036740.
%K A366672 nonn,easy
%O A366672 0,2
%A A366672 _Paulius Dilkas_, Oct 15 2023