A223023 Poly-Cauchy numbers c_n^(-5).

1, 32, 211, 359, -538, 984, -1866, 1110, 32640, -449760, 5035200, -55896960, 646005600, -7896549120, 102604234080, -1418189492640, 20828546505600, -324419255412480, 5346952977432960, -93035974518691200, 1705088403923592960, -32842738382065931520

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_{k=0..n} Stirling1(n,k)*(k+1)^5.

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