A225436 Denominators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ ...)))).

1, 3, 3, 9, 12, 39, 123, 87, 771, 1473, 11427, 46779, 19533, 212559, 1890093, 8691981, 1570137, 9863961, 486463449, 2459255649, 6337494039, 16694653089, 7166066763, 51605000913, 2729643372111, 7738039298811, 89176449644619, 104501330075607, 1554311845035993, 361227369257943

Offset: 1

Author

Eric W. Weisstein, May 07 2013

Keywords

• nonn
• frac

Comments

1

Examples

			1, 1/3, 2/3, 4/9, 7/12, 19/39, ... = A225435(n)/A225436(n).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..843
• Eric Weisstein's World of Mathematics, Continued Fraction Constants
• Eric Weisstein's World of Mathematics, Generalized Continued Fraction

Crossrefs

Cf. A225435 (numerators).

Cf. A111129 (decimal digits of infinite c.f.).

Related to A000932.

Programs

Mathematica

Denominator[Table[ContinuedFractionK[k, 1, {k, 1, n}], {n, 30}]]

Formula

E.g.f: (1/2)*(2+e^((1/2)*(1+z)^2)*sqrt(2*Pi)*(1+z)*(-erf(1/sqrt(2))+erf((1+z)/sqrt(2)))).

Limit_{n->oo} A225435(n)/a(n) = sqrt(2/(e*Pi))/erfc(1/sqrt(2))-1 = A111129.