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A225436
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Denominators 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, 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
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OFFSET
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1,2
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COMMENTS
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1
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LINKS
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FORMULA
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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.
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EXAMPLE
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MATHEMATICA
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Denominator[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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