OFFSET
0,2
COMMENTS
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).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Takao Komatsu, Poly-Cauchy numbers, RIMS Kokyuroku 1806 (2012)
Takao Komatsu, Poly-Cauchy numbers with a q parameter, Ramanujan J. 31 (2013), 353-371.
Takao Komatsu, Poly-Cauchy numbers, Kyushu J. Math. 67 (2013), 143-153.
T. Komatsu, V. Laohakosol, K. Liptai, A generalization of poly-Cauchy numbers and its properties, Abstract and Applied Analysis, Volume 2013, Article ID 179841, 8 pages.
Takao Komatsu, FZ Zhao, The log-convexity of the poly-Cauchy numbers, arXiv preprint arXiv:1603.06725, 2016
MATHEMATICA
Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^4, {k, 0, n}]], {n, 0, 25}]
PROG
(PARI) a(n) = denominator(sum(k=0, n, (-1)^k*stirling(n, k, 1)/(k+1)^4)); \\ Michel Marcus, Nov 15 2015
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Takao Komatsu, Mar 31 2013
STATUS
approved