cp's OEIS Frontend

A224109 Numerators of poly-Cauchy numbers of the second kind hat c_n^(5).

%I A224109 #40 Feb 27 2023 03:23:28
%S A224109 1,-1,275,-6289,92902541,-154473289,13399738273333,-377635608584803,
%T A224109 822223497000264427,-1492945924219675973,1323386773861946436609781,
%U A224109 -2448418399924413951578983,177825546947844845937070681472647
%N A224109 Numerators of poly-Cauchy numbers of the second kind hat c_n^(5).
%C A224109 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 A224109 Vincenzo Librandi, <a href="/A224109/b224109.txt">Table of n, a(n) for n = 0..260</a>
%H A224109 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 A224109 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 A224109 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%H A224109 Takao 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 A224109 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 A224109 Table[Numerator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
%o A224109 (PARI) a(n) = numerator(sum(k=0, n,(-1)^k*stirling(n, k, 1)/(k+1)^5)); \\ _Michel Marcus_, Nov 15 2015
%Y A224109 Cf. A002657, A223904, A224107, A224102, A224104, A224106, A224107 (denominators).
%K A224109 sign,frac
%O A224109 0,3
%A A224109 _Takao Komatsu_, Mar 31 2013