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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
OFFSET
0,2
COMMENTS
Definition of poly-Cauchy numbers in A222627.
LINKS
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
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k)*(k+1)^4.
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: A330824 A189806 A378166 * A283271 A031446 A294584
KEYWORD
sign
AUTHOR
Takao Komatsu, Mar 28 2013
STATUS
approved