The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A173948 a(n) = denominator of (Zeta(2, 1/4) - Zeta(2, n+1/4)), where Zeta is the Hurwitz Zeta function. 13
 1, 1, 25, 2025, 342225, 98903025, 4846248225, 121156205625, 101892368930625, 12328976640605625, 16878369020989100625, 28372538324282678150625, 28372538324282678150625, 1390254377889851229380625, 3905224547492592103330175625, 1409786061644825749302193400625, 5245813935380396613153461643725625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Presumably conjectures: For n>=2 numbers in this sequence are divisible by 25. For n>=7 numbers in this sequence are divisible by 25^2. LINKS G. C. Greubel, Table of n, a(n) for n = 0..250 FORMULA a(n) = denominator of 8*Catalan + Pi^2 - Zeta(2, (4*n + 1)/4), with the Hurwitz Zeta function, and Catalan is given in A006752. [See the name with Zeta(2, 1/4) = Psi(1, 1/4) = 8*Catalan + Pi^2, and the Trigamma function Psi(1, z).] MAPLE r := n -> Psi(1, 1/4) - Zeta(0, 2, n+1/4): seq(denom(simplify(r(n))), n=0..16); # Peter Luschny, Nov 14 2017 MATHEMATICA Table[Denominator[FunctionExpand[8*Catalan + Pi^2 - Zeta[2, (4*n + 1)/4]]], {n, 0, 20}] (* Vaclav Kotesovec, Nov 14 2017 *) Denominator[Table[Sum[1/(4*k + 1)^2, {k, 0, n-1} ], {n, 0, 20}]] (* Vaclav Kotesovec, Nov 14 2017 *) PROG (PARI) for(n=0, 20, print1(denominator(sum(k=0, n-1, 1/(4*k+1)^2)), ", ")) \\ G. C. Greubel, Aug 22 2018 (Magma) [1] cat [Denominator((&+[1/(4*k+1)^2: k in [0..n-1]])): n in [1..20]]; // G. C. Greubel, Aug 22 2018 CROSSREFS Cf. A006752, A120268, A173945, A173947 (numerators). Sequence in context: A197671 A051112 A061843 * A279276 A197408 A197430 Adjacent sequences:  A173945 A173946 A173947 * A173949 A173950 A173951 KEYWORD frac,nonn AUTHOR Artur Jasinski, Mar 03 2010 EXTENSIONS Name simplified by Peter Luschny, Nov 14 2017 Formula reformulated. - Wolfdieter Lang, Nov 14 2017. STATUS approved

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

Last modified November 26 04:03 EST 2022. Contains 358353 sequences. (Running on oeis4.)