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 A362968 #13 Jun 22 2023 06:04:36
%S A362968 1,3,19,201,3081,62683,1598955,49180113,1773405649,73410669171,
%T A362968 3432267261699,178922825114905,10291053760222041,647436905815864011,
%U A362968 44229766376059342171,3260749830852693615777,258039101519624535653025
%N A362968 Number of integral points in 2 * permutohedron of order n.
%C A362968 Every vectorial sum of two permutations represents an integral point in 2*permutohedron, however the converse does not hold. Hence, a(n) >= A175176(n) for all n, where the equality holds only for n <= 5.
%C A362968 Number of points up to their components order is given by A007747.
%H A362968 C. Bebeacua, T. Mansour, A. Postnikov, and S. Severini. <a href="https://arxiv.org/abs/math/0506334">On the X-rays of permutations</a>, arXiv:math/0506334 [math.CO], 2005.
%H A362968 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutohedron">Permutohedron</a>.
%F A362968 a(n) = Sum_{k=0..n-1} A138464(n,k) * 2^k, which is the value of the Ehrhart polynomial of permutohedron at t = 2.
%F A362968 E.g.f.: exp(-W(-2*x)/2 - W(-2*x)^2/4), where W() is the Lambert function.
%p A362968 w := LambertW(-2*x): egf := exp(-w * (2 + w) / 4): ser := series(egf, x, 20):
%p A362968 seq(n! * coeff(ser, x, n), n = 1..17); # _Peter Luschny_, Jun 19 2023
%o A362968 (PARI) a362968(n) = my(x=y+O(y^(n+1))); n! * polcoef( exp(-lambertw(-2*x)/2 - lambertw(-2*x)^2/4), n );
%Y A362968 Cf. A007747, A138464, A175176, A362967.
%K A362968 nonn
%O A362968 1,2
%A A362968 _Max Alekseyev_, Jun 17 2023