A219247 Denominators of poly-Cauchy numbers of the second kind hat c_n^(2).

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

Author

Takao Komatsu, Mar 31 2013

Keywords

• nonn
• frac

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

Crossrefs

Cf. A002790, A223899, A224102 (numerators).

Programs

Mathematica

Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^2, {k, 0, n}]], {n, 0, 25}]

PARI

a(n) = denominator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^2)); \\ Michel Marcus, Nov 14 2015