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 A360820 #12 Mar 14 2023 15:07:21
%S A360820 1,4,48,1792,221184,98566144,173946175488,1281755680079872,
%T A360820 39534286378918477824,5018464395368794081460224,
%U A360820 2586745980900067184722499862528,5375203895735606878055792019528220672,44865714160227204455469409035569750630989824,1501355804811017489524770237231795462175548447391744
%N A360820 a(n) = Sum_{k=0..n} binomial(n, k)*2^(n^2-k*(n-k)).
%C A360820 This is the model count of the following sentence in first-order logic: forall X. forall Y. friends(X, Y) /\ smokes(X) -> smokes(Y).
%H A360820 G. Van den Broeck, W. Meert, and A. Darwiche, <a href="https://arxiv.org/abs/1312.5378">Skolemization for weighted first-order model counting</a>, arXiv:1312.5378 [cs.AI], 2013-2014.
%F A360820 a(n) = Sum_{k=0..n} binomial(n, k)*2^(n^2-k*(n-k)).
%F A360820 a(n) ~ 2^(n^2 + 1). - _Vaclav Kotesovec_, Feb 22 2023
%e A360820 If the domain is {1}, then all four interpretations ({}, {smokes(1)}, {friends(1, 1)}, {smokes(1), friends(1, 1)}) are models, so a(1) = 4.
%t A360820 a[n_] := Sum[Binomial[n, k]*2^(n^2 - k*(n - k)), {k, 0, n}]; Array[a, 14, 0] (* _Amiram Eldar_, Feb 24 2023 *)
%o A360820 (PARI) a(n) = sum(k=0, n, binomial(n, k)*2^(n^2-k*(n-k))); \\ _Michel Marcus_, Feb 22 2023
%K A360820 nonn,easy
%O A360820 0,2
%A A360820 _Paulius Dilkas_, Feb 21 2023