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A055546
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a(n) = (-1)^(n+1) * 2^n * n!^2.
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7
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-1, 2, -16, 288, -9216, 460800, -33177600, 3251404800, -416179814400, 67421129932800, -13484225986560000, 3263182688747520000, -939796614359285760000, 317651255653438586880000, -124519292216147926056960000, 56033681497266566725632000000
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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Sum_{n>=0} |a(n)|/(2*n+1)! = Pi/2. - Daniel Suteu, Feb 06 2017
Sum_{n>=0} 1/a(n) = (-1) * A334383.
Sum_{n>=0} (-1)^(n+1)/a(n) = A334381. (End)
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MATHEMATICA
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Table[(-1)^(n+1)2^n n!^2, {n, 0, 20}]
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PROG
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CROSSREFS
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Row of A340591 (in absolute values).
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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