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 A208528 Number of permutations of n>1 having exactly 3 points P on the boundary of their bounding square. 4
 0, 4, 16, 72, 384, 2400, 17280, 141120, 1290240, 13063680, 145152000, 1756339200, 22992076800, 323805081600, 4881984307200, 78460462080000, 1339058552832000, 24186745110528000, 460970906812416000, 9245027631071232000, 194632160654131200000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS A bounding square for a permutation of n is the square with sides parallel to the coordinate axis containing (1,1) and (n,n), and the set of points P of a permutation p is the set {(k,p(k)) for 0=3} 1/a(n) = (Ei(1) - gamma)/4, where Ei(1) = A091725 and gamma = A001620. Sum_{n>=3} (-1)^(n+1)/a(n) = (gamma - Ei(-1))/4, where Ei(-1) = -A099285. (End) EXAMPLE a(3) = 4 because {(1,1),(2,3),(3,2)}, {(1,3),(2,1),(3,2)}, {(1,2),(2,3),(3,1)} and {(1,2),(2,1),(3,3)} each have three points on the bounding square. MATHEMATICA Table[(4n-8)(n-2)!, {n, 2, 10}] PROG (Python) import math def a(n):     return (4*n-8)*math.factorial(n-2) CROSSREFS Cf. A098916, A208529. Cf. A001620, A091725, A099285. Sequence in context: A217461 A129872 A059371 * A007234 A096244 A030131 Adjacent sequences:  A208525 A208526 A208527 * A208529 A208530 A208531 KEYWORD nonn AUTHOR David Nacin, Feb 27 2012 STATUS approved

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Last modified July 2 07:08 EDT 2022. Contains 354985 sequences. (Running on oeis4.)