The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A120077 Denominators of row sums of rational triangle A120072/A120073. 4
 4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 1270080, 153679680, 153679680, 25971865920, 25971865920, 129859329600, 519437318400, 150117385017600, 150117385017600, 54192375991353600, 2167695039654144, 1548353599752960, 221193371393280, 117011293467045120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 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. The n for which a(n) differs from A007407(n) are given by A309829. - Jeppe Stig Nielsen, Aug 18 2019 LINKS Jeppe Stig Nielsen, Table of n, a(n) for n = 2..1150 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: log(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,..]. PROG (PARI) a(n) = denominator(sum(j=1, n-1, 1/j^2-1/n^2)) \\ Jeppe Stig Nielsen, Aug 18 2019 (PARI) a(n) = denominator(sum(j=1, n, 1/j^2) - 1/n) \\ Jeppe Stig Nielsen, Aug 18 2019 CROSSREFS Cf. A309829. Sequence in context: A103931 A334580 A068589 * A007407 A051418 A069046 Adjacent sequences:  A120074 A120075 A120076 * A120078 A120079 A120080 KEYWORD nonn,easy,frac AUTHOR Wolfdieter Lang, Jul 20 2006 EXTENSIONS a(21)-a(23) from Jeppe Stig Nielsen, Aug 18 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 18 13:54 EDT 2021. Contains 347527 sequences. (Running on oeis4.)