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A219247
Denominators of poly-Cauchy numbers of the second kind hat c_n^(2).
4
1, 4, 36, 48, 1800, 240, 35280, 20160, 226800, 50400, 3659040, 665280, 1967565600, 2242240, 129729600, 34594560, 2677989600, 66830400, 1857684628800, 39109150080, 3226504881600, 307286179200, 2333316585600, 1285014931200, 2192556726360000, 25057791158400
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
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)^2, {k, 0, n}]], {n, 0, 25}]
PROG
(PARI) a(n) = denominator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^2)); \\ Michel Marcus, Nov 14 2015
CROSSREFS
Cf. A002790, A223899, A224102 (numerators).
Sequence in context: A062182 A308531 A073771 * A224094 A367511 A280934
KEYWORD
nonn,frac
AUTHOR
Takao Komatsu, Mar 31 2013
STATUS
approved