cp's OEIS Frontend

A224104 Numerators of poly-Cauchy numbers of the second kind hat c_n^(3).

%I A224104 #36 Feb 26 2023 18:12:19
%S A224104 1,-1,35,-217,135989,-236881,435876493,-3174551347,790667708347,
%T A224104 -1473406853309,11050163107919893,-20886680047664287,
%U A224104 9154917271574968829623,-277315386220087376401,803143323197313772705
%N A224104 Numerators of poly-Cauchy numbers of the second kind hat c_n^(3).
%C A224104 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 A224104 Vincenzo Librandi, <a href="/A224104/b224104.txt">Table of n, a(n) for n = 0..300</a>
%H A224104 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 A224104 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 A224104 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%H A224104 T. Komatsu, V. Laohakosol, 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 A224104 Takao Komatsu, FZ Zhao, <a href="http://arxiv.org/abs/1603.06725">The log-convexity of the poly-Cauchy numbers</a>, arXiv preprint arXiv:1603.06725, 2016
%t A224104 Table[Numerator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^3, {k, 0, n}]], {n, 0,
%t A224104   25}]
%o A224104 (PARI) a(n) = numerator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^3)); \\ _Michel Marcus_, Nov 14 2015
%Y A224104 Cf. A002657, A223901, A224102, A224103 (denominators).
%K A224104 sign,frac
%O A224104 0,3
%A A224104 _Takao Komatsu_, Mar 31 2013