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A326177 Denominators of a recurrence relation arising in impact dynamics. 1
1, 2, 2, 20, 5, 700, 350, 7000, 1750, 215600, 215600, 12512500, 350350000, 7007000000, 1001000000, 45815000000, 148898750000, 121989767900000000, 121989767900000000, 30497441975000000, 4879590716000000, 5106491684294000000000, 464226516754000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

André S. Carvalho, Jorge M. Martins, Exact restitution and generalizations for the Hunt-Crossley contact model, Mechanism and Machine Theory, (2019) 139, 174-194.

FORMULA

Initial terms are

B(0) = 0,

B(1) = -3/2.

Subsequent terms are computed from

B(n) = 1/(2*(n+2)) * ( (6-7*n)*B(n-1) - 3*(n-1)*B(n-2) + 2*r(n) ),

where r(n) denotes a finite sum given by

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) ).

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

y(x) = Sum_{n=1..oo} B(n)*(x-1)^n.

MATHEMATICA

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}]]]]

CROSSREFS

Cf. A326176 (numerators).

Sequence in context: A141084 A172194 A093777 * A103129 A322898 A009340

Adjacent sequences:  A326174 A326175 A326176 * A326178 A326179 A326180

KEYWORD

nonn,frac

AUTHOR

André S. Carvalho, Jun 11 2019

STATUS

approved

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)