This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A223899 #34 Apr 15 2025 08:26:22
%S A223899 1,-4,13,-51,244,-1392,9260,-70508,605320,-5788008,61021872,
%T A223899 -703384272,8801449344,-118828732032,1721888828928,-26656798602240,
%U A223899 439110126743040,-7669109089082880,141557837068938240,-2753560001544053760,56299265625742848000
%N A223899 Poly-Cauchy numbers of the second kind hat c_n^(-2).
%H A223899 Vincenzo Librandi, <a href="/A223899/b223899.txt">Table of n, a(n) for n = 0..300</a>
%H A223899 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 A223899 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), p. 42-53.
%H A223899 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%F A223899 a(n) = Sum_{k=0..n} (-1)^k * (k+1)^2 * Stirling1(n,k).
%F A223899 E.g.f.: (1 - log(1 + x) * (3 - log(1 + x))) / (1 + x). - _Ilya Gutkovskiy_, Aug 09 2021
%F A223899 From _Seiichi Manyama_, Apr 15 2025: (Start)
%F A223899 E.g.f.: Sum_{k>=0} (k+1)^2 * (-log(1+x))^k / k!.
%F A223899 a(n) = (-1)^n * Sum_{k=0..2} k! * Stirling2(3,k+1) * |Stirling1(n+1,k+1)|. (End)
%t A223899 Table[Sum[StirlingS1[n, k] (-1)^k (k + 1)^2, {k, 0, n}], {n, 0, 30}]
%o A223899 (Magma) [&+[StirlingFirst(n, k)*(-1)^k*(k+1)^2: k in [0..n]]: n in [0..23]]; // _Vincenzo Librandi_, Aug 03 2013
%o A223899 (PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*(-1)^k*(k+1)^2); \\ _Michel Marcus_, Nov 14 2015
%Y A223899 Cf. A081046, A223901, A223902, A223904.
%Y A223899 Cf. A222627.
%K A223899 sign
%O A223899 0,2
%A A223899 _Takao Komatsu_, Mar 29 2013