A224109 Numerators of poly-Cauchy numbers of the second kind hat c_n^(5).

1, -1, 275, -6289, 92902541, -154473289, 13399738273333, -377635608584803, 822223497000264427, -1492945924219675973, 1323386773861946436609781, -2448418399924413951578983, 177825546947844845937070681472647

Offset

0,3

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..260

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A002657, A223904, A224107, A224102, A224104, A224106, A224107 (denominators).

Sequence in context: A257123 A130292 A133536 * A075666 A121743 A084802

Adjacent sequences: A224106 A224107 A224108 * A224110 A224111 A224112

Keyword

sign,frac

Author

Takao Komatsu, Mar 31 2013

Status

approved