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A225435
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Numerators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ ...)))).
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4
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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
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OFFSET
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1,3
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LINKS
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FORMULA
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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))).
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EXAMPLE
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MATHEMATICA
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Numerator[Table[ContinuedFractionK[k, 1, {k, 1, n}], {n, 30}]]
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CROSSREFS
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Cf. A111129 (decimal digits of infinite c.f.).
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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