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A075829
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Let u(1)=x, u(n+1)=(n^2/u(n))+1; then u(n)=(b(n)*x+c(n))/(d(n)*x+a(n)).
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5
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1, 0, 1, 1, 5, 13, 23, 101, 307, 641, 893, 7303, 9613, 97249, 122989, 19793, 48595, 681971, 818107, 13093585, 77107553, 66022193, 76603673, 1529091919, 1752184789, 7690078169, 8719737569, 23184641107, 3721854001, 96460418429
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| for x real >0 lim n -> infinity abs(u(n)-n) = (x-1)/(1+(x-1)*ln(2))
Difference between denominator and numerator of the (n-1)-th alternating harmonic number Sum[(-1)^(k+1)*1/k,{k,1,n-1}] = A058313(n-1)/A058312(n-1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 22 2006
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FORMULA
| a(n)=A024168(n-1)/gcd(A024168(n-1), A024168(n)). - Michael Somos, Oct 29, 2002
a(n) = A058312(n-1) - A058313(n-1) for n>1; a(1)=1. a(n) = Denominator[Sum[(-1)^(k+1)*1/k,{k,1,n-1}]] - Numerator[Sum[(-1)^(k+1)*1/k,{k,1,n-1}]]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 22 2006
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MATHEMATICA
| Denominator[Table[Sum[(-1)^(k+1)*1/k, {k, 1, n-1}], {n, 1, 30}]]-Numerator[Table[Sum[(-1)^(k+1)*1/k, {k, 1, n-1}], {n, 1, 30}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 22 2006
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PROG
| (PARI) u(n)=if(n<2, x, (n-1)^2/u(n-1)+1); a(n)=polcoeff(denominator(u(n)), 0, x)
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CROSSREFS
| Cf. A075827 A075828 A075830
Cf. A058312, A058313.
Sequence in context: A099958 A049833 * A119248 A114998 A140090 A121511
Adjacent sequences: A075826 A075827 A075828 * A075830 A075831 A075832
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 14 2002
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