A224096
Denominators of poly-Cauchy numbers c_n^(3).
Original entry on oeis.org
1, 8, 216, 576, 108000, 14400, 14817600, 16934400, 571536000, 127008000, 101428588800, 18441561600, 709031939616000, 12120204096000, 6678479808000, 24932991283200, 229679599076928000, 818822100096000
Offset: 0
- 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
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Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^3, {k, 0, n}]], {n, 0, 25}]
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a(n) = denominator(sum(k=0, n, stirling(n, k, 1)/(k+1)^3)); \\ Michel Marcus, Nov 15 2015
A224099
Numerators of poly-Cauchy numbers c_n^(4).
Original entry on oeis.org
1, 1, -65, 635, -1691507, 2602903, -30316306813, 405644259179, -281598937164737, 491752927006687, -38273845811539969069, 68624716189056755839, -372590717516807448774422779
Offset: 0
- 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
-
Table[Numerator[Sum[StirlingS1[n, k]/ (k + 1)^4, {k, 0, n}]], {n, 0, 25}]
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a(n) = numerator(sum(k=0, n,stirling(n, k, 1)/(k+1)^4)); \\ Michel Marcus, Nov 15 2015
A224101
Numerators of poly-Cauchy numbers c_n^(5).
Original entry on oeis.org
1, 1, -211, 4241, -57453709, 29825987, -7362684132917, 198504470798947, -415989828245529323, 730328251215062341, -628191544925589374756597, 1131010588175721446183783, -80125844020238574218022657310343
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..250
- 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, 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.
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Table[Numerator[Sum[StirlingS1[n, k]/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
-
a(n) = numerator(sum(k=0, n, stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015
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