cp's OEIS Frontend

A224100 Denominators of poly-Cauchy numbers c_n^(5).

%I A224100 #42 Mar 02 2025 14:02:33
%S A224100 1,32,7776,82944,388800000,51840000,2613824640000,11948912640000,
%T A224100 3629482214400000,806551603200000,77937565348177920000,
%U A224100 14170466426941440000,92074412343521441433600000
%N A224100 Denominators of poly-Cauchy numbers c_n^(5).
%C A224100 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 A224100 Vincenzo Librandi, <a href="/A224100/b224100.txt">Table of n, a(n) for n = 0..300</a>
%H A224100 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 A224100 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 A224100 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%H A224100 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 A224100 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 A224100 Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
%o A224100 (PARI) a(n) = denominator(sum(k=0, n, stirling(n, k, 1)/(k+1)^5)); \\ _Michel Marcus_, Nov 15 2015
%Y A224100 Cf. A006233, A223023, A224094, A224096, A224098, A224101 (numerators).
%K A224100 nonn,frac
%O A224100 0,2
%A A224100 _Takao Komatsu_, Mar 31 2013