A224097
Numerators of poly-Cauchy numbers c_n^(3).
Original entry on oeis.org
1, 1, -19, 89, -46261, 23323, -114895757, 760567603, -174446569403, 302339104957, -2125170096355349, 3788248001789087, -1573899862241140688567, 317684785943639774839, -2242333884754953400123
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[Numerator[Sum[StirlingS1[n, k]/ (k + 1)^3, {k, 0, n}]], {n, 0, 25}]
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a(n) = numerator(sum(k=0, n,stirling(n, k, 1)/(k+1)^3)); \\ Michel Marcus, Nov 15 2015
A224098
Denominators of poly-Cauchy numbers c_n^(4).
Original entry on oeis.org
1, 16, 1296, 6912, 6480000, 2592000, 6223392000, 14224896000, 1440270720000, 320060160000, 2811600481536000, 511200087552000, 255506749760021760000, 291175783202304000, 16846598885276160000
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, 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.
-
Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^4, {k, 0, n}]], {n, 0, 25}]
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a(n) = denominator(sum(k=0, n,stirling(n, k, 1)/(k+1)^4)); \\ Michel Marcus, Nov 15 2015
A224100
Denominators of poly-Cauchy numbers c_n^(5).
Original entry on oeis.org
1, 32, 7776, 82944, 388800000, 51840000, 2613824640000, 11948912640000, 3629482214400000, 806551603200000, 77937565348177920000, 14170466426941440000, 92074412343521441433600000
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, 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.
-
Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
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a(n) = denominator(sum(k=0, n, stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015
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