A224094 Denominators of poly-Cauchy numbers c_n^(2).

1, 4, 36, 48, 1800, 720, 35280, 20160, 226800, 10080, 731808, 665280, 1967565600, 11211200, 129729600, 34594560, 18745927200, 28641600, 371536925760, 3990729600, 3226504881600, 4877558400, 466663317120, 550720684800, 2192556726360000, 175404538108800

Offset: 0

Author

Takao Komatsu, Mar 30 2013

Keywords

• nonn
• frac

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

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• 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

Crossrefs

Cf. A006233, A222627, A224095 (numerators).

Programs

Mathematica

Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^2, {k, 0, n}]], {n, 0, 25}]

PARI

a(n) = denominator(sum(k=0, n,stirling(n, k, 1)/(k+1)^2)); \\ Michel Marcus, Nov 15 2015