A231121 Denominators of coefficients of expansion of arctan(x)^3.

1, 1, 15, 945, 175, 17325, 23648625, 1576575, 7309575, 1283268987, 3360942585, 1932541986375, 135664447443525, 218461268025, 242856109621125, 27604644460267875, 4479480941961650625, 1151866527932995875, 31580724596338947904875, 809762169136896100125, 4742892704944677157875

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

Let u(n) = (-1)^n/(2n+1) and P(n,x) = u(n) + x*Sum_{i=0..n-1} u(i)*P(n-i-1,x)), with P(0,x) = u(0). Then, the terms are the denominators of the coefficients of x^2 in each polynomial.

Mathematica

a[n_] := SeriesCoefficient[ArcTan[x]^3, {x, 0, 2*n+3}] // Denominator
(* or *) a[n_] := 3*Sum[2^(i-2)*Binomial[2*(n+1), i-1]*StirlingS1[i, 3]/i!, {i, 3, 2n+3}] // Denominator; Table[a[n], {n, 0, 20}] (* from the formula given by Ruperto Corso in A002429 *)
Take[Denominator[CoefficientList[Series[ArcTan[x]^3, {x, 0, 50}], x] ], {4, -1, 2}] (* Harvey P. Dale, Apr 07 2017 *)

Crossrefs

Cf. A002428, A002429, A071968, A140749, A141904, A142048, A081051.

Sequence in context: A324423 A261067 A136419 * A103639 A055413 A067408

Adjacent sequences: A231118 A231119 A231120 * A231122 A231123 A231124

Keyword

nonn,frac

Author

Jean-François Alcover and Paul Curtz, Nov 04 2013

Status

approved