The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A101627 Numerator of partial sums of a certain series. 5
 1, 39, 241, 34883, 14039, 1516871, 7601151, 875425657, 7887002813, 7095769757767, 14199583385459, 75087685321529, 75113436870869, 927229349730873529, 927436191807263569, 305182576081725442901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The denominators are given in A101628. Second member (m=3) of a family defined in A101028. The limit s=lim(s(n),n->infty) with the s(n) defined below equals 8*sum(Zeta(2*k+1)/3^(2*k),k=1..infty) with Euler's (or Riemann's) Zeta function. This limit is 12*(log(3)-1) = 1.18334746...; see the Abramowitz-Stegun (given in A101028) reference p. 259, eq. 6.3.15 with z=1/3 together with p. 258. LINKS M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. W. Lang: Rationals s(n) and more. FORMULA a(n)=numerator(s(n)) with s(n)=24*sum(1/((3*k-1)*(3*k)*(3*k+1)), k=1..n). EXAMPLE s(3)= 24*(1/(2*3*4)+ 1/(5*6*7) + 1/(8*9*10)) = 241/210, hence a(3)=241 and A101628(3)=210. MATHEMATICA Numerator[Accumulate[Table[8/(9k^3-k), {k, 20}]]] CROSSREFS Cf. A101028, A101629, A101631 members m=2, 4, 5, resp. Sequence in context: A266104 A190538 A190606 * A229639 A070146 A327344 Adjacent sequences:  A101624 A101625 A101626 * A101628 A101629 A101630 KEYWORD nonn,frac,easy AUTHOR Wolfdieter Lang, Dec 23 2004 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 December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)