login

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 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Denominators of poly-Cauchy numbers of the second kind hat c_n^(2).
4

%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