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A223023 Poly-Cauchy numbers c_n^(-5). 4
1, 32, 211, 359, -538, 984, -1866, 1110, 32640, -449760, 5035200, -55896960, 646005600, -7896549120, 102604234080, -1418189492640, 20828546505600, -324419255412480, 5346952977432960, -93035974518691200, 1705088403923592960, -32842738382065931520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Definition of poly-Cauchy numbers in A222627.

LINKS

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

FORMULA

a(n) = sum(stirling1(n,k)*(k+1)^5, k=0..n).

MATHEMATICA

Table[Sum[StirlingS1[n, k] (k + 1)^5, {k, 0, n}], {n, 0, 25}]

PROG

(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

CROSSREFS

Sequence in context: A247928 A184020 A283336 * A119286 A125342 A126500

Adjacent sequences:  A223020 A223021 A223022 * A223024 A223025 A223026

KEYWORD

sign

AUTHOR

Takao Komatsu, Mar 28 2013

STATUS

approved

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)