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 A059615 a(n) is the number of non-parallel lines determined by a pair of vertices (extreme points) in the polytope of real n X n doubly stochastic matrices. The vertices are the n! permutation matrices. 2
 0, 1, 15, 240, 6040, 217365, 10651011, 681667840, 55215038880, 5521504648185, 668102052847735, 96206695728917136, 16258931576714668920, 3186750589054271109325, 717018882536990087693835 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES M. Marcus, Hermitian Forms and Eigenvalues, in Survey of Numerical Analysis, J. Todd, ed. McGraw-Hill, New York, 1962. LINKS FORMULA a(n) = (1/2)*Sum_{k=0...n-2} binomial(n,k)^2 * (n-k)! * d(n-k) for n >= 2, where d(n) is the number of derangements of n elements: permutations of n elements with no fixed points - sequence A000166. Using the formula: d(n) = n!*Sum_{k=0..n} (-1)^k/k!, a(n) = (1/2)*Sum_{k=0..n-2} ((n!/k!)^2 * Sum_{m=0..n-k} (-1)^m/m!). EXAMPLE a(3) = 15 because there are 3! = 6 vertices and C(6,2) lines and in this case all are nonparallel so a(3) = C(6,2) = 15. MAPLE Digits := 200: with(combinat): d := n->n!*sum((-1)^j/j!, j=0..n): a059615 := n->1/2*sum( binomial(n, k)^2 * (n-k)!*d(n-k), k=0..n-2): for n from 1 to 30 do printf(`%d, `, round(evalf(a059615(n)))) od: PROG (PARI) a(n) = (1/2)*sum(k=0, n-2, ((n!/k!)^2 * sum(m=0, n-k, (-1)^m/m!))); \\ Michel Marcus, Mar 14 2018 CROSSREFS Cf. A000166, A059760. Sequence in context: A154806 A133199 A059760 * A215855 A163031 A065920 Adjacent sequences:  A059612 A059613 A059614 * A059616 A059617 A059618 KEYWORD nonn AUTHOR Noam Katz (noamkj(AT)hotmail.com), Feb 18 2001 EXTENSIONS More terms from James A. Sellers, Feb 19 2001 Offset corrected by Michel Marcus, Mar 14 2018 STATUS approved

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Last modified April 2 18:43 EDT 2020. Contains 333189 sequences. (Running on oeis4.)