A224105 Denominators of poly-Cauchy numbers of the second kind hat c_n^(4).

1, 16, 1296, 6912, 6480000, 288000, 6223392000, 14224896000, 1440270720000, 64012032000, 562320096307200, 511200087552000, 255506749760021760000, 1455878916011520000, 673863955411046400, 17969705477627904000

Offset

0,2

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.

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

Mathematica

Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^4, {k, 0, n}]], {n, 0, 25}]

Prog

(PARI) a(n) = denominator(sum(k=0, n, (-1)^k*stirling(n, k, 1)/(k+1)^4)); \\ Michel Marcus, Nov 15 2015

Crossrefs

Cf. A002790, A223902, A219247, A224103, A224106 (numerators).

Sequence in context: A308587 A363921 A027648 * A224098 A016828 A072161

Adjacent sequences: A224102 A224103 A224104 * A224106 A224107 A224108

Keyword

nonn,frac

Author

Takao Komatsu, Mar 31 2013

Status

approved