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A055546
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(-1)^(n+1)*2^n*n!^2.
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1
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-1, 2, -16, 288, -9216, 460800, -33177600, 3251404800, -416179814400, 67421129932800, -13484225986560000, 3263182688747520000, -939796614359285760000, 317651255653438586880000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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. [From Wolfdieter Lang, Jan 10 2012]
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REFERENCES
| A. L. Mackay, On the regular heptagon, J. Math. Chemistry, vol. 21, 1997, 197-209.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| E.g.f.: -arcsinh(x/sqrt(2))^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 30 2004
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MATHEMATICA
| Table[(-1)^(n+1)2^n n!^2, {n, 0, 20}]
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CROSSREFS
| Sequence in context: A102599 A123744 A136796 * A009549 A009795 A112722
Adjacent sequences: A055543 A055544 A055545 * A055547 A055548 A055549
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KEYWORD
| sign
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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