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A222748 Poly-Cauchy numbers c_n^(-4). 3
1, 16, 65, 45, -116, 340, -1240, 5480, -28464, 169248, -1125840, 8197680, -63806016, 514314240, -4058967744, 26952984000, -37203513984, -4251686488704, 140692872720384, -3560137793538048, 84004474130786304, -1955196907518928896, 45927815909901004800 (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)^4, k=0..n).

MATHEMATICA

Table[Sum[StirlingS1[n, k] (k + 1)^4, {k, 0, n}], {n, 0, 25}]

PROG

(MAGMA) [&+[StirlingFirst(n, k)*(k+1)^4: 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)^4); \\ Michel Marcus, Nov 14 2015

CROSSREFS

Sequence in context: A327496 A330824 A189806 * A283271 A031446 A294584

Adjacent sequences:  A222745 A222746 A222747 * A222749 A222750 A222751

KEYWORD

sign

AUTHOR

Takao Komatsu, Mar 28 2013

STATUS

approved

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Last modified October 31 05:06 EDT 2020. Contains 338098 sequences. (Running on oeis4.)