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
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 12 2005
EXTENSIONS
More terms from Alois P. Heinz, Nov 18 2009
STATUS
approved