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 A059760 #15 Jul 02 2025 16:02:00
%S A059760 0,0,1,15,240,5040,147240,5959800,323850240,22800476160,2017745251200,
%T A059760 219066851203200,28615863103027200,4425987756321331200,
%U A059760 799788468703877452800,166940001463941433728000,39857401887591969128448000,10792266259145851457961984000
%N A059760 a(n) is the number of edges (one-dimensional faces) in the convex polytope of real n X n doubly stochastic matrices.
%C A059760 The vertices are the n! permutation matrices. If A(p1) and A(p2) are two permutation matrices corresponding to permutations p1 and p2 the closed interval between these two matrices forms an edge of the polytope iff the permutation p1*(p2^-1) is a cycle, i.e. its cycle decomposition in the symmetric group S_n contains exactly one nontrivial cycle.
%H A059760 Alois P. Heinz, <a href="/A059760/b059760.txt">Table of n, a(n) for n = 0..250</a>
%F A059760 a(n) = 1/2* n! * Sum_{k=2...n} C(n,k)*(k-1)!.
%F A059760 a(n) ~ Pi * n^(2*n) / exp(2*n - 1). - _Vaclav Kotesovec_, Jun 09 2019
%e A059760 a(3) = 15 because there are 3! = 6 vertices and C(6,2) intervals and in this case all are edges so a(3) = C(6,2) = 15.
%p A059760 with(combinat): for n from 1 to 30 do printf(`%d,`,1/2* n! * sum(binomial(n,k)*(k-1)!, k=2..n)) od:
%t A059760 a[n_] = If[n==0, 0, (n*n!/2)*(HypergeometricPFQ[{1, 1, 1-n}, {2}, -1]-1)]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 19 2017 *)
%Y A059760 Cf. A059615.
%Y A059760 Note that b(n) = (Sum k=2...n C(n,k)*(k-1)!) gives sequence A006231.
%K A059760 nonn
%O A059760 0,4
%A A059760 Noam Katz (noamkj(AT)hotmail.com), Feb 20 2001
%E A059760 More terms from _James Sellers_, Feb 21 2001