A224103 Denominators of poly-Cauchy numbers of the second kind hat c_n^(3).

1, 8, 216, 576, 108000, 43200, 14817600, 16934400, 571536000, 127008000, 101428588800, 18441561600, 709031939616000, 1731457728000, 373994869248, 24932991283200, 229679599076928000, 491293260057600

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)^3, {k, 0, n}]], {n, 0, 25}]

Prog

(PARI) a(n) = denominator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^3)); \\ Michel Marcus, Nov 14 2015

Crossrefs

Cf. A002790, A223901, A219247, A224104 (numerators).

Sequence in context: A247032 A027646 A224096 * A072159 A016827 A239222

Adjacent sequences: A224100 A224101 A224102 * A224104 A224105 A224106

Keyword

nonn,frac

Author

Takao Komatsu, Mar 31 2013

Status

approved