A223907 Poly-Cauchy numbers of the second kind hat c_4^(-n).

74, 244, 854, 3148, 12134, 48604, 201254, 857548, 3745574, 16712764, 75954854, 350674348, 1640943014, 7766839324, 37118063654, 178831601548, 867439996454, 4231277324284, 20735541791654, 102002862327148, 503340513737894, 2490084124103644, 12344177045442854

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

Conjecture: a(n) = 3*2^(1+n)+3*2^(1+2*n)+11*3^n+5^n. G.f.: -2*x*(1440*x^3-1346*x^2+396*x-37) / ((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Mar 31 2013

Mathematica

Table[Sum[StirlingS1[4, k] (-1)^k (k + 1)^n, {k, 0, 4}], {n, 30}]

Prog

(PARI) a(n) = sum(k=0, 4, (-1)^k*stirling(4, k, 1)*(k+1)^n); \\ Michel Marcus, Nov 15 2015

Crossrefs

Cf. A223851.

Sequence in context: A121809 A204361 A204354 * A232512 A046833 A205754

Adjacent sequences: A223904 A223905 A223906 * A223908 A223909 A223910

Keyword

nonn

Author

Takao Komatsu, Mar 29 2013

Status

approved