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 A055546 a(n) = (-1)^(n+1) * 2^n * n!^2. 7
 -1, 2, -16, 288, -9216, 460800, -33177600, 3251404800, -416179814400, 67421129932800, -13484225986560000, 3263182688747520000, -939796614359285760000, 317651255653438586880000, -124519292216147926056960000, 56033681497266566725632000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Coefficient of the Cayley-Menger determinant of order n. A roller coaster has n rows of seats, each of which has room for two people. |a(n)| is the number of ways n men and n women can be seated with a man and a woman in each row. - Geoffrey Critzer, Dec 17 2011 The o.g.f. of 1/a(n) is -BesselI(0,i*sqrt(2*x)), with i the imaginary unit. See Abramowitz-Stegun (reference and link under A008277), p. 375, 9.6.10. - Wolfdieter Lang, Jan 10 2012 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 Paul C. Kainen, Construction numbers: How to build a graph?, arXiv:2302.13186 [math.CO], 2023. Usman A. Khan, Soummya Kar and Jose M. F. Moura, A novel geometric approach towards a linear theory for sensor localization, 2013. Alan L. Mackay, On the regular heptagon, J. Math. Chemistry, vol. 21, 1997, 197-209. Eric Weisstein's World of Mathematics, Cayley-Menger Determinant. FORMULA E.g.f.: -arcsinh(x/sqrt(2))^2. - Vladeta Jovovic, Aug 30 2004 Sum_{n>=0} |a(n)|/(2*n+1)! = Pi/2. - Daniel Suteu, Feb 06 2017 a(n) = (-1)^(n+1) * A000079(n) * A001044(n). - Terry D. Grant, May 21 2017 From Amiram Eldar, Nov 18 2020: (Start) Sum_{n>=0} 1/a(n) = (-1) * A334383. Sum_{n>=0} (-1)^(n+1)/a(n) = A334381. (End) MATHEMATICA Table[(-1)^(n+1)2^n n!^2, {n, 0, 20}] PROG (PARI) a(n)={(-1)^(n+1) * 2^n * n!^2} \\ Andrew Howroyd, Nov 07 2019 CROSSREFS Cf. A000079, A001044, A019669, A334381, A334383. Row of A340591 (in absolute values). Sequence in context: A102599 A123744 A136796 * A009549 A254744 A009795 Adjacent sequences: A055543 A055544 A055545 * A055547 A055548 A055549 KEYWORD sign AUTHOR Eric W. Weisstein EXTENSIONS Terms a(14) and beyond from Andrew Howroyd, Nov 07 2019 STATUS approved

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Last modified June 24 00:50 EDT 2024. Contains 373661 sequences. (Running on oeis4.)