A224102
Numerators of poly-Cauchy numbers of the second kind hat c_n^(2).
Original entry on oeis.org
1, -1, 13, -43, 5647, -3401, 2763977, -10326059, 876576493, -1665984623, 1156096889861, -2220482068331, 75970695882225719, -1088498788093641, 855021689397409453, -3324381371618385007, 4010325276269988793421
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] (-1)^k/ (k + 1)^2, {k, 0, n}]], {n, 0,
25}]
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a(n) = numerator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^2)); \\ Michel Marcus, Nov 14 2015
A224103
Denominators of poly-Cauchy numbers of the second kind hat c_n^(3).
Original entry on oeis.org
1, 8, 216, 576, 108000, 43200, 14817600, 16934400, 571536000, 127008000, 101428588800, 18441561600, 709031939616000, 1731457728000, 373994869248, 24932991283200, 229679599076928000, 491293260057600
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[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^3, {k, 0, n}]], {n, 0, 25}]
-
a(n) = denominator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^3)); \\ Michel Marcus, Nov 14 2015
A224105
Denominators of poly-Cauchy numbers of the second kind hat c_n^(4).
Original entry on oeis.org
1, 16, 1296, 6912, 6480000, 288000, 6223392000, 14224896000, 1440270720000, 64012032000, 562320096307200, 511200087552000, 255506749760021760000, 1455878916011520000, 673863955411046400, 17969705477627904000
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] (-1)^k/ (k + 1)^4, {k, 0, n}]], {n, 0, 25}]
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a(n) = denominator(sum(k=0, n,(-1)^k*stirling(n, k, 1)/(k+1)^4)); \\ Michel Marcus, Nov 15 2015
A224107
Denominators of poly-Cauchy numbers of the second kind hat c_n^(5).
Original entry on oeis.org
1, 32, 7776, 82944, 388800000, 155520000, 2613824640000, 11948912640000, 3629482214400000, 806551603200000, 77937565348177920000, 14170466426941440000, 92074412343521441433600000, 524640526173911347200000, 6070840374298117017600000, 12951126131835982970880000
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.
- 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.
-
Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
-
a(n) = denominator(sum(k=0, n,(-1)^k*stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015
Showing 1-4 of 4 results.
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