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A223902
Poly-Cauchy numbers of the second kind hat c_n^(-4).
4
1, -16, 97, -531, 3148, -20940, 156680, -1310840, 12166096, -124281120, 1387313520, -16813355280, 219967479744, -3090914335104, 46439677053120, -743069262651840, 12616998421804416, -226608929801923968, 4292762009479969536, -85545808260446050560, 1789078468694176410624
OFFSET
0,2
COMMENTS
The poly-Cauchy numbers of the second kind hat c_n^k can be expressed in terms of the (unsigned) Stirling numbers of the first kind: hat c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))/(m+1)^k, m=0..n).
LINKS
Takao Komatsu, Poly-Cauchy numbers with a q parameter, Ramanujan J. 31 (2013), 353-371.
Takao Komatsu, Poly-Cauchy numbers, RIMS Kokyuroku 1806 (2012), p. 42-53.
Takao Komatsu, Poly-Cauchy numbers, Kyushu J. Math. 67 (2013), 143-153.
MATHEMATICA
Table[Sum[StirlingS1[n, k] (-1)^k (k + 1)^4, {k, 0, n}], {n, 0, 30}]
PROG
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*(-1)^k*(k+1)^4); \\ Michel Marcus, Nov 14 2015
CROSSREFS
Cf. A222749.
Sequence in context: A277225 A265841 A248883 * A264580 A122102 A214612
KEYWORD
sign
AUTHOR
Takao Komatsu, Mar 29 2013
STATUS
approved