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A120077
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Denominators of row sums of rational triangle A120072/A120073.
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3
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4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 1270080, 153679680, 153679680, 25971865920, 25971865920, 129859329600, 519437318400, 150117385017600, 150117385017600, 54192375991353600, 2167695039654144
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| The first 19 terms coincide with A007407(n), for n>=2. However a(20)=2167695039654144 and A007407(20)=10838475198270720= 5*a(20). Also a(21)=1548353599752960 and A007407(21)=221193371393280 = a(21)/7. From n=22 up to at least n=100 (checked) both sequences coincide again.
See the W. Lang link under A120072 for more details.
The corresponding numerators are given by A120076.
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FORMULA
| a(n)=denominator(r(m)), with the rationals r(m):=sum(A120072(m,n)/A120073(m,n),n=1..m-1),m>=2.
The rationals are r(m) = Zeta(2;m-1) - (m-1)/m^2, m>=2, with the partial sums Zeta(2;n):=sum(1/k^2,k=1..n). See the W. Lang link under A103345.
O.g.f. for the rationals r(m), m>=2: ln(1-x) + polylog(2,x)/(1-x).
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EXAMPLE
| The rationals A120076(m)/A120077(m), m>=2, begin with [3/4, 37/36, 169/144, 4549/3600, 4769/3600,..].
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CROSSREFS
| Sequence in context: A102263 A103931 A068589 * A007407 A051418 A069046
Adjacent sequences: A120074 A120075 A120076 * A120078 A120079 A120080
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KEYWORD
| nonn,easy,frac
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
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