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A224101
Numerators of poly-Cauchy numbers c_n^(5).
2
1, 1, -211, 4241, -57453709, 29825987, -7362684132917, 198504470798947, -415989828245529323, 730328251215062341, -628191544925589374756597, 1131010588175721446183783, -80125844020238574218022657310343
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
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)^5, {k, 0, n}]], {n, 0, 25}]
PROG
(PARI) a(n) = numerator(sum(k=0, n, stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015
CROSSREFS
Cf. A006232, A223023, A224095, A224097, A224099, A224100 (denominators).
Sequence in context: A330426 A271979 A185719 * A013529 A229519 A289983
KEYWORD
sign,frac
AUTHOR
Takao Komatsu, Mar 31 2013
STATUS
approved