|
%I #34 Feb 26 2023 13:22:11
%S 1,4,36,48,1800,240,35280,20160,226800,50400,3659040,665280,
%T 1967565600,2242240,129729600,34594560,2677989600,66830400,
%U 1857684628800,39109150080,3226504881600,307286179200,2333316585600,1285014931200,2192556726360000,25057791158400
%N Denominators of poly-Cauchy numbers of the second kind hat c_n^(2).
%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 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="http://link.springer.com/article/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 T. Komatsu, V. Laohakosol, 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, FZ Zhao, <a href="http://arxiv.org/abs/1603.06725">The log-convexity of the poly-Cauchy numbers</a>, arXiv preprint arXiv:1603.06725, 2016
%t Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^2, {k, 0, n}]], {n, 0, 25}]
%o (PARI) a(n) = denominator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^2)); \\ _Michel Marcus_, Nov 14 2015
%Y Cf. A002790, A223899, A224102 (numerators).
%K nonn,frac
%O 0,2
%A _Takao Komatsu_, Mar 31 2013
|
