A105216 Maximum denominator among the n! ratios equal to the continued fractions which have the permutations of (1,2,3,...,n) for terms.

1, 2, 7, 31, 164, 1021, 7340, 59899, 547423, 5541311, 61560751, 744810564, 9749580487, 137299957892, 2069988277027, 33266800950301, 567742165061876, 10254686071781119, 195439907769223706, 3919618523321600065, 82517650453354285621, 1819502802723019762607

Offset

1,2

Comments

Calculated by Vladeta Jovovic and David W. Wilson.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Formula

a(n) ~ c * n!, where c = 1.69579254611555585961617066333... . - Vaclav Kotesovec, Aug 25 2014

From Mark van Hoeij, Jul 08 2024: (Start)

Conjecture: a(n) = n*a(n-1) + (n-1)*a(n-3) + a(n-4).

Consequently: a(n) = round( sqrt(2/Pi) * (exp(-1)*BesselI(1,1)+ sinh(1)*BesselI(0,1)) * BesselK(n/2+1/2,1) * BesselK(n/2+1,1) ). (End)

Consequently: c = exp(-1)*BesselI(1,1)+ sinh(1)*BesselI(0,1). - Vaclav Kotesovec, Jul 09 2024

Maple

r:= proc(l) local j; infinity; for j to nops(l) do l[j] +1/% od end: gl:= proc(n) local i, l; l:=[]; for i from 2 to n do l:= `if` (irem (i, 2)=0, [l[], i], [i, l[]]) od; [l[], 1] end: a:= n-> denom (r (gl (n))): seq (a(n), n=1..25);  # Alois P. Heinz, Nov 18 2009

Mathematica

r[l_] := Module[{j, f = Infinity}, For[j = 1, j <=  Length[l], j++, f = l[[j]] + 1/f]; f];
gl[n_] := Module[{i, l = {}}, For[i = 2, i <= n, i++, l = If[Mod [i, 2] == 0, Append[l, i], Prepend[l, i]]]; Append[l, 1]];
a[n_] := Denominator [r[gl[n]]];
Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *)

Crossrefs

Cf. A105151.

Sequence in context: A277396 A227119 A002872 * A260532 A193657 A007164

Adjacent sequences: A105213 A105214 A105215 * A105217 A105218 A105219

Keyword

nonn

Author

Leroy Quet, Apr 12 2005

Extensions

More terms from Alois P. Heinz, Nov 18 2009

Status

approved