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

1,1

Comments

See A335828 for details.

Links

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

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+ *)

Crossrefs

Cf. A335828 (numerators).

Sequence in context: A009698 A012724 A012624 * A061307 A061300 A079264

Adjacent sequences: A335826 A335827 A335828 * A335830 A335831 A335832

Keyword

nonn,frac

Author

Amiram Eldar, Jun 25 2020

Status

approved