A230145 Denominator of 1/v_n(1/2), where polynomial v_n(x) is used to approximate x->sin(Pi*x)/Pi.

3, 75, 595, 333795, 25638459, 5788790007, 898772045457, 1467030741832227, 126774706022852173, 244108884436744360605, 94974266622893811200463, 176151264858556860995936775, 95962705639251788100721754775, 121363236202656183485569513082175

Offset: 1

Author

Alois P. Heinz, Oct 10 2013

Keywords

• nonn
• frac

Comments

Coefficients of v_n are given by the n-th row of A144859/A144860.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..99

Crossrefs

Numerators are given in A230144.

Cf. A000796.

Programs

Maple

v:= proc(n) option remember; local f, i, x; f:= unapply(simplify(sum('cat(a||(2*i+1)) *x^(2*i+1)', 'i'=0..n) ), x); unapply(subs(solve({f(1)=0, `if`(n=0, NULL, D(f)(0)=1), seq((D@@i)(f)(1)=-(D@@i)(f)(0), i=2..n)}, {seq(cat(a||(2*i+1)), i=0..n)}), sum('cat(a||(2*i+1)) *x^(2*i+1)', 'i'=0..n) ), x) end: seq(denom(1/v(n)(1/2)), n=1..15);

Mathematica

v[n_] := v[n] = Module[{f, i, x, a}, f[x_] := Sum[a[2*i+1]*x^(2*i+1), {i, 0, n}]; Function[x, Sum[a[2*i+1]*x^(2*i+1), {i, 0, n}] /. First @ Solve[Join[{f[1] == 0}, {If[n == 0, True, f'[0] == 1]}, Table[Derivative[i][f][1] == -Derivative[i][f][0], {i, 2, n}]]]]]; Table[Denominator[1/v[n][1/2]], {n, 1, 15}] (* Jean-François Alcover, Feb 13 2014, after Maple *)