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%I #39 Feb 27 2023 03:32:32
%S 1,32,7776,82944,388800000,155520000,2613824640000,11948912640000,
%T 3629482214400000,806551603200000,77937565348177920000,
%U 14170466426941440000,92074412343521441433600000,524640526173911347200000,6070840374298117017600000,12951126131835982970880000
%N Denominators of poly-Cauchy numbers of the second kind hat c_n^(5).
%C The poly-Cauchy numbers of the second kind hat c_n^(k) can be expressed in terms of the (unsigned) Stirling numbers of the first kind: hat c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))/(m+1)^k, m=0..n).
%H Vincenzo Librandi, <a href="/A224107/b224107.txt">Table of n, a(n) for n = 0..300</a>
%H 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 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 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%H Takao 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 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 Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
%o (PARI) a(n) = denominator(sum(k=0, n,(-1)^k*stirling(n, k, 1)/(k+1)^5)); \\ _Michel Marcus_, Nov 15 2015
%Y Cf. A002790, A223904, A219247, A224103, A224105, A224109 (numerators).
%K nonn,frac
%O 0,2
%A _Takao Komatsu_, Mar 31 2013
%E More terms from _Michel Marcus_, Nov 15 2015
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