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

 

Logo


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.

License Agreements, Terms of Use, Privacy Policy. .

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