A036243 Denominator of fraction equal to the continued fraction [ 0, 2, 4, ...2n ].

1, 2, 9, 56, 457, 4626, 55969, 788192, 12667041, 228794930, 4588565641, 101177239032, 2432842302409, 63355077101666, 1776375001149057, 53354605111573376, 1709123738571497089, 58163561716542474402, 2095597345534100575561

Offset: 0

Author

Jeff Burch

Keywords

• frac
• nonn

Crossrefs

Cf. A036242 (numerator), A369585.

Programs

Maple

b := n -> BesselK(n,1)*BesselI(0,1)-(-1)^n*BesselI(n,1)* BesselK(0,1);
A036243 := n -> b(n+1):
seq(simplify(A036243(n)), n=0..18); # Peter Luschny, Sep 14 2014

Mathematica

Table[Denominator[FromContinuedFraction[Range[0,2n,2]]],{n,0,20}] (* Harvey P. Dale, Feb 18 2016 *)

PARI

a(n)=contfracpnqn(vector(n+1,i,2*i-2))[2,1];
vector(22,n,a(n-1)) \\ M. F. Hasler, Feb 08 2011; edited by Michel Marcus, Feb 12 2024

Formula

a(n) = b(n+1) where b(n) = K(n,1)*I(0,1) - (-1)^n*I(n,1)*K(0,1), K(n,x) and I(n,x) Bessel functions. - Peter Luschny, Sep 14 2014

a(n) = Sum_{0..n} |A369585(n)|. - Peter Luschny, Jan 30 2024

a(n) = 2*n*a(n-1) + a(n-2). - Christian Krause, Aug 18 2024

Extensions

a(0) = 1 prepended by Peter Luschny, Jan 30 2024