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A223908
Poly-Cauchy numbers of the second kind -hat c_5^(-n).
1
394, 1392, 5248, 20940, 87784, 384252, 1747048, 8213820, 39780424, 197799612, 1006785448, 5232061500, 27696448264, 149034102972, 813659961448, 4499466577980, 25163809551304, 142131488326332, 809773455691048, 4648490027827260, 26859776918289544
OFFSET
1,1
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.
FORMULA
Empirical g.f.: -2*x*(43200*x^4-48390*x^3+19239*x^2-3244*x+197) / ((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Mar 31 2013
MATHEMATICA
Table[-Sum[StirlingS1[5, k] (-1)^k (k + 1)^n, {k, 0, 5}], {n, 30}]
PROG
(PARI) a(n) = -sum(k=0, 5, (-1)^k*stirling(5, k, 1)*(k+1)^n); \\ Michel Marcus, Nov 14 2015
CROSSREFS
Cf. A223852.
Sequence in context: A236234 A252691 A051986 * A251256 A270843 A267965
KEYWORD
nonn,easy
AUTHOR
Takao Komatsu, Mar 29 2013
STATUS
approved