|
Search: id:A120077
|
|
| |
|
| 4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 1270080, 153679680, 153679680, 25971865920, 25971865920, 129859329600, 519437318400, 150117385017600, 150117385017600, 54192375991353600, 2167695039654144
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
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.
|
|
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).
|
|
EXAMPLE
|
The rationals A120076(m)/A120077(m), m>=2, begin with [3/4, 37/36, 169/144, 4549/3600, 4769/3600,..].
|
|
CROSSREFS
|
Sequence in context: A102263 A103931 A068589 this_sequence A007407 A051418 A069046
Adjacent sequences: A120074 A120075 A120076 this_sequence A120078 A120079 A120080
|
|
KEYWORD
|
nonn,easy,frac
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
|
|
|
Search completed in 0.002 seconds
|
