A224097 Numerators of poly-Cauchy numbers c_n^(3).

1, 1, -19, 89, -46261, 23323, -114895757, 760567603, -174446569403, 302339104957, -2125170096355349, 3788248001789087, -1573899862241140688567, 317684785943639774839, -2242333884754953400123

Offset

0,3

Comments

The poly-Cauchy numbers c_n^(k) can be expressed in terms of the (unsigned) Stirling numbers of the first kind: c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))*(-1)^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]/ (k + 1)^3, {k, 0, n}]], {n, 0, 25}]

Prog

(PARI) a(n) = numerator(sum(k=0, n, stirling(n, k, 1)/(k+1)^3)); \\ Michel Marcus, Nov 15 2015

Crossrefs

Cf. A006232, A222636, A224095, A224096 (denominators).

Sequence in context: A201306 A160296 A347364 * A088574 A096031 A302710

Adjacent sequences: A224094 A224095 A224096 * A224098 A224099 A224100

Keyword

sign,frac

Author

Takao Komatsu, Mar 31 2013

Status

approved