cp's OEIS Frontend

A224101 Numerators of poly-Cauchy numbers c_n^(5).

%I A224101 #40 Mar 02 2025 14:02:09
%S A224101 1,1,-211,4241,-57453709,29825987,-7362684132917,198504470798947,
%T A224101 -415989828245529323,730328251215062341,-628191544925589374756597,
%U A224101 1131010588175721446183783,-80125844020238574218022657310343
%N A224101 Numerators of poly-Cauchy numbers c_n^(5).
%C A224101 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).
%H A224101 Vincenzo Librandi, <a href="/A224101/b224101.txt">Table of n, a(n) for n = 0..250</a>
%H A224101 Takao Komatsu, <a href="http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1806-06.pdf">Poly-Cauchy numbers</a>, RIMS Kokyuroku 1806 (2012)
%H A224101 Takao Komatsu, <a href="https://doi.org/10.1007/s11139-012-9452-0">Poly-Cauchy numbers with a q parameter</a>, Ramanujan J. 31 (2013), 353-371.
%H A224101 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%H A224101 T. Komatsu, V. Laohakosol, and K. Liptai, <a href="http://dx.doi.org/10.1155/2013/179841">A generalization of poly-Cauchy numbers and its properties</a>, Abstract and Applied Analysis, Volume 2013, Article ID 179841, 8 pages.
%H A224101 Takao Komatsu and F.-Z. Zhao, <a href="http://arxiv.org/abs/1603.06725">The log-convexity of the poly-Cauchy numbers</a>, arXiv preprint arXiv:1603.06725 [math.NT], 2016.
%t A224101 Table[Numerator[Sum[StirlingS1[n, k]/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
%o A224101 (PARI) a(n) = numerator(sum(k=0, n, stirling(n, k, 1)/(k+1)^5)); \\ _Michel Marcus_, Nov 15 2015
%Y A224101 Cf. A006232, A223023, A224095, A224097, A224099, A224100 (denominators).
%K A224101 sign,frac
%O A224101 0,3
%A A224101 _Takao Komatsu_, Mar 31 2013