A225435 - OEIS

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A225435

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

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).