A223908 Poly-Cauchy numbers of the second kind -hat c_5^(-n).

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A223905 A223906 A223907 * A223909 A223910 A223911

Keyword

nonn,easy

Author

Takao Komatsu, Mar 29 2013

Status

approved