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A347051
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a(0) = 1, a(1) = 2; a(n) = n * (n+1) * a(n-1) + a(n-2).
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2
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1, 2, 13, 158, 3173, 95348, 4007789, 224531532, 16170278093, 1455549559902, 160126621867313, 21138169636045218, 3297714589844921321, 600205193521411725640, 126046388354086307305721, 30251733410174235165098680, 8228597533955746051214146681, 2517981097123868465906693983066
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OFFSET
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0,2
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COMMENTS
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a(n) is the denominator of fraction equal to the continued fraction [0; 2, 6, 12, 20, 30, ..., n*(n+1)].
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LINKS
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FORMULA
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a(n) ~ c * n^(2*n + 2) / exp(2*n), where c = 6.9478401587876967481571909904361736371398357108358019737901443045685048723... - Vaclav Kotesovec, Aug 14 2021
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EXAMPLE
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a(1) = 2 because 1/(1*2) = 1/2.
a(2) = 13 because 1/(1*2 + 1/(2*3)) = 6/13.
a(3) = 158 because 1/(1*2 + 1/(2*3 + 1/(3*4))) = 73/158.
a(4) = 3173 because 1/(1*2 + 1/(2*3 + 1/(3*4 + 1/(4*5)))) = 1466/3173.
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MATHEMATICA
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a[0] = 1; a[1] = 2; a[n_] := a[n] = n (n + 1) a[n - 1] + a[n - 2]; Table[a[n], {n, 0, 17}]
Table[Denominator[ContinuedFractionK[1, k (k + 1), {k, 1, n}]], {n, 0, 17}]
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CROSSREFS
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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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