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A223023
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Poly-Cauchy numbers c_n^(-5).
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4
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1, 32, 211, 359, -538, 984, -1866, 1110, 32640, -449760, 5035200, -55896960, 646005600, -7896549120, 102604234080, -1418189492640, 20828546505600, -324419255412480, 5346952977432960, -93035974518691200, 1705088403923592960, -32842738382065931520
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OFFSET
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0,2
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COMMENTS
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Definition of poly-Cauchy numbers in A222627.
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LINKS
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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, Some recurrence relations of poly-Cauchy numbers, J. Nonlinear Sci. Appl., (2019) Vol. 12, Issue 12, 829-845.
M. Z. Spivey,Combinatorial sums and finite differences, Discr. Math. 307 (24) (2007) 3130-3146
Wikipedia, Stirling transform
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FORMULA
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a(n) = Sum_{k=0..n} Stirling1(n,k)*(k+1)^5.
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MATHEMATICA
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Table[Sum[StirlingS1[n, k] (k + 1)^5, {k, 0, n}], {n, 0, 25}]
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PROG
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(Magma) [&+[StirlingFirst(n, k)*(k+1)^5: k in [0..n]]: n in [0..25]]; // Bruno Berselli, Mar 28 2013
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*(k+1)^5); \\ Michel Marcus, Nov 14 2015
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CROSSREFS
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Sequence in context: A247928 A184020 A283336 * A119286 A125342 A126500
Adjacent sequences: A223020 A223021 A223022 * A223024 A223025 A223026
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KEYWORD
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sign
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AUTHOR
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Takao Komatsu, Mar 28 2013
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STATUS
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approved
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