cp's OEIS Frontend

A224106 Numerators of poly-Cauchy numbers of the second kind hat c_n^(4).

%I A224106 #40 Mar 02 2025 14:02:41
%S A224106 1,-1,97,-1147,3472243,-653983,74118189437,-1058923294571,
%T A224106 777910456216513,-285577840060819,23240203016832136201,
%U A224106 -216925341603548096639,1222007019804929270080450811
%N A224106 Numerators of poly-Cauchy numbers of the second kind hat c_n^(4).
%C A224106 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).
%H A224106 Vincenzo Librandi, <a href="/A224106/b224106.txt">Table of n, a(n) for n = 0..300</a>
%H A224106 Takao Komatsu, <a href="http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1806-06.pdf">Poly-Cauchy numbers</a>, RIMS Kokyuroku 1806 (2012)
%H A224106 Takao Komatsu, <a href="http://link.springer.com/article/10.1007/s11139-012-9452-0">Poly-Cauchy numbers with a q parameter</a>, Ramanujan J. 31 (2013), 353-371.
%H A224106 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%H A224106 T. Komatsu, V. Laohakosol, and K. Liptai, <a href="http://dx.doi.org/10.1155/2013/179841">A generalization of poly-Cauchy numbers and its properties</a>, Abstract and Applied Analysis, Volume 2013, Article ID 179841, 8 pages.
%H A224106 Takao Komatsu and F.-Z. Zhao, <a href="http://arxiv.org/abs/1603.06725">The log-convexity of the poly-Cauchy numbers</a>, arXiv preprint arXiv:1603.06725 [math.NT], 2016.
%t A224106 Table[Numerator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^4, {k, 0, n}]], {n, 0,
%t A224106   25}]
%o A224106 (PARI) a(n) = numerator(sum(k=0, n,(-1)^k*stirling(n, k, 1)/(k+1)^4)); \\ _Michel Marcus_, Nov 15 2015
%Y A224106 Cf. A002657, A223902, A224105, A114102, A224104, A224105 (denominators).
%K A224106 sign,frac
%O A224106 0,3
%A A224106 _Takao Komatsu_, Mar 31 2013