A335829 Denominators of coefficients in a power series expansion of the distance between two bodies falling freely towards each other along a straight line under the influence of their mutual gravitational attraction.

2, 12, 360, 5040, 113400, 29937600, 2724321600, 14859936000, 12504636144000, 2375880867360000, 4390627842881280000, 605906642317616640000, 8950893579692064000000, 74435631008719204224000000, 32379499488792853837440000000, 8030115873220627751685120000000

Offset: 1

Author

Amiram Eldar, Jun 25 2020

Keywords

• nonn
• frac

Comments

See A335828 for details.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..238

Crossrefs

Cf. A335828 (numerators).

Programs

Mathematica

c[1] = 1/2; c[n_] := c[n] = (2*Sum[(n - k)*(2*n - 2*k - 1)*c[n - k]*c[k], {k, 1, n - 1}] - Sum[(n - m)*(2*n - 2*m - 1)*c[n - m]*c[m - k]*c[k], {m, 2, n - 1}, {k, 1, m - 1}])/(n*(2*n - 1)); Denominator @ Array[c, 16]
(* or *)
Quiet[-Denominator @ CoefficientList[AsymptoticDSolveValue[{y[x]*y'[x]^2 == 2*(1-y[x]), y[0] == 1}, y[x], {x, 0, 25}], x][[3;;-1;;2]]] (* requires Mathematica 11.3+ *)