A224102 Numerators of poly-Cauchy numbers of the second kind hat c_n^(2).

1, -1, 13, -43, 5647, -3401, 2763977, -10326059, 876576493, -1665984623, 1156096889861, -2220482068331, 75970695882225719, -1088498788093641, 855021689397409453, -3324381371618385007, 4010325276269988793421

Offset

0,3

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

Prog

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

Crossrefs

Cf. A002657, A223899, A219247 (denominators).

Sequence in context: A144236 A082689 A228505 * A123294 A015247 A033652

Adjacent sequences: A224099 A224100 A224101 * A224103 A224104 A224105

Keyword

sign,frac

Author

Takao Komatsu, Mar 31 2013

Status

approved