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A225435
Numerators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ ...)))).
4
1, 1, 2, 4, 7, 19, 68, 44, 416, 758, 6092, 24284, 10348, 110864, 997828, 4545476, 827252, 5166356, 255994804, 1289266004, 3332578444, 8757252244, 3766552348, 27079574548, 1434303566956, 4061479240156, 46849154788124, 54858398447372, 816458740546228, 189647639388428
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Continued Fraction Constants
Eric Weisstein's World of Mathematics, Generalized Continued Fraction
FORMULA
E.g.f.: (1/2)*(-2+e^((1/2)*z*(2+z))*(1+z)(2+sqrt(2*e*Pi)*erf(1/sqrt(2)))-e^((1/2)*(1+z)^2)*sqrt(2*Pi)*(1+z)*erf((1+z)/sqrt(2))).
Lim_{n->infinity} A225435(n)/A225436(n) = sqrt(2/(e*Pi))/erfc(1/sqrt(2))-1 = A111129.
EXAMPLE
1, 1/3, 2/3, 4/9, 7/12, 19/39, ... = A225435(n)/A225436(n).
MATHEMATICA
Numerator[Table[ContinuedFractionK[k, 1, {k, 1, n}], {n, 30}]]
CROSSREFS
Cf. A225436 (denominators).
Cf. A111129 (decimal digits of infinite c.f.).
Related to A000932.
Sequence in context: A276027 A367440 A101569 * A243049 A247234 A327444
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, May 07 2013
STATUS
approved