A224107 Denominators of poly-Cauchy numbers of the second kind hat c_n^(5).

1, 32, 7776, 82944, 388800000, 155520000, 2613824640000, 11948912640000, 3629482214400000, 806551603200000, 77937565348177920000, 14170466426941440000, 92074412343521441433600000, 524640526173911347200000, 6070840374298117017600000, 12951126131835982970880000

Offset: 0

Author

Takao Komatsu, Mar 31 2013

Keywords

• nonn
• frac

Comments

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).

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.
• Takao Komatsu, V. Laohakosol and K. Liptai, A generalization of poly-Cauchy numbers and its properties, Abstract and Applied Analysis, Volume 2013, Article ID 179841, 8 pages.
• Takao Komatsu and F. Z. Zhao, The log-convexity of the poly-Cauchy numbers, arXiv preprint arXiv:1603.06725 [math.NT], 2016.

Crossrefs

Cf. A002790, A223904, A219247, A224103, A224105, A224109 (numerators).

Programs

Mathematica

Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]

PARI

a(n) = denominator(sum(k=0, n,(-1)^k*stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015

Extensions

More terms from Michel Marcus, Nov 15 2015