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%I #21 Sep 13 2019 22:45:15
%S 1,2,2,20,5,700,350,7000,1750,215600,215600,12512500,350350000,
%T 7007000000,1001000000,45815000000,148898750000,121989767900000000,
%U 121989767900000000,30497441975000000,4879590716000000,5106491684294000000000,464226516754000000000
%N Denominators of a recurrence relation arising in impact dynamics.
%H André S. Carvalho, Jorge M. Martins, <a href="https://doi.org/10.1016/j.mechmachtheory.2019.03.028">Exact restitution and generalizations for the Hunt-Crossley contact model</a>, Mechanism and Machine Theory, (2019) 139, 174-194.
%F Initial terms are
%F B(0) = 0,
%F B(1) = -3/2.
%F Subsequent terms are computed from
%F B(n) = 1/(2*(n+2)) * ( (6-7*n)*B(n-1) - 3*(n-1)*B(n-2) + 2*r(n) ),
%F where r(n) denotes a finite sum given by
%F r(n) = Sum_{j=2..n-1} B(j)*( (n-j)*B(n-j-1) + (3*n-3*j+1)*B(n-j) + 2*(n-j+1)*B(n-j+1) ).
%F Finally, the present sequence is given by the denominators of B(n), which is employed to compute the inverse restitution, through an infinite sum, given by
%F y(x) = Sum_{n=1..oo} B(n)*(x-1)^n.
%t Denominator@With[{m = 22}, Module[{B}, Join[{B[0] = 0}, {B[1] = -3/2}, Table[B[n] = 1/(2 (n + 2)) ((6 - 7 n) B[n - 1] - 3 (n - 1) B[n - 2] + 2 Sum[B[j] ((n - j) B[n - j - 1] + (3 n - 3 j + 1) B[n - j] + 2 (n - j + 1) B[n - j + 1]), {j, 2, n - 1}]), {n, 2, m}]]]]
%Y Cf. A326176 (numerators).
%K nonn,frac
%O 0,2
%A _André S. Carvalho_, Jun 11 2019
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