A335829 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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