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!)
 A224101 Numerators of poly-Cauchy numbers c_n^(5). 2
 1, 1, -211, 4241, -57453709, 29825987, -7362684132917, 198504470798947, -415989828245529323, 730328251215062341, -628191544925589374756597, 1131010588175721446183783, -80125844020238574218022657310343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The poly-Cauchy numbers c_n^(k) can be expressed in terms of the (unsigned) Stirling numbers of the ﬁrst kind: c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))*(-1)^m/(m+1)^k, m=0..n). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..250 Takao Komatsu, Poly-Cauchy numbers, RIMS Kokyuroku 1806 (2012) Takao Komatsu, Poly-Cauchy numbers with a q parameter, Ramanujan J. 31 (2013), 353-371. Takao Komatsu, Poly-Cauchy numbers, Kyushu J. Math. 67 (2013), 143-153. T. Komatsu, V. Laohakosol, K. Liptai, A generalization of poly-Cauchy numbers and its properties, Abstract and Applied Analysis, Volume 2013, Article ID 179841, 8 pages. Takao Komatsu, FZ Zhao, The log-convexity of the poly-Cauchy numbers, arXiv preprint arXiv:1603.06725, 2016 MATHEMATICA Table[Numerator[Sum[StirlingS1[n, k]/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}] PROG (PARI) a(n) = numerator(sum(k=0, n, stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015 CROSSREFS Cf. A006232, A223023, A224095, A224097, A224099, A224100 (denominators). Sequence in context: A071367 A271979 A185719 * A013529 A229519 A289983 Adjacent sequences: A224098 A224099 A224100 * A224102 A224103 A224104 KEYWORD sign,frac AUTHOR Takao Komatsu, Mar 31 2013 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 29 11:53 EST 2022. Contains 358424 sequences. (Running on oeis4.)