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
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.
Programs
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Mathematica
Table[Numerator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}] -
PARI
a(n) = numerator(sum(k=0, n,(-1)^k*stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015
Comments