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A055546 a(n) = (-1)^(n+1) * 2^n * n!^2. 2
-1, 2, -16, 288, -9216, 460800, -33177600, 3251404800, -416179814400, 67421129932800, -13484225986560000, 3263182688747520000, -939796614359285760000, 317651255653438586880000 (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

Table of n, a(n) for n=0..13.

Usman A. Khan, Soummya Kar and Jose M. F. Moura, A novel geometric approach towards a linear theory for sensor localization, 2013.

A. 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

MATHEMATICA

Table[(-1)^(n+1)2^n n!^2, {n, 0, 20}]

CROSSREFS

Cf. A000079, A001044, A019669.

Sequence in context: A102599 A123744 A136796 * A009549 A254744 A009795

Adjacent sequences:  A055543 A055544 A055545 * A055547 A055548 A055549

KEYWORD

sign

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified September 20 21:03 EDT 2019. Contains 327247 sequences. (Running on oeis4.)