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A223904 Poly-Cauchy numbers of the second kind hat c_n^(-5). 4
1, -32, 275, -1817, 12134, -87784, 699894, -6158058, 59566464, -630057696, 7246806720, -90151868160, 1207028135520, -17314992935040, 265048030579680, -4313510679824160, 74387763047472000, -1355291635314213120, 26016022725597866880, -524865277479851360640, 11103724030717930095360 (list; graph; refs; listen; history; text; internal format)
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

Vincenzo Librandi, Table of n, a(n) for n = 0..300

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)^5, {k, 0, n}], {n, 0, 30}]

PROG

(MAGMA) [&+[StirlingFirst(n, k)*(-1)^k*(k+1)^5: k in [0..n]]: n in [0..23]]; // Vincenzo Librandi, Aug 03 2013

(PARI) a(n) = sum(k=0, n, (-1)^k*stirling(n, k, 1)*(k+1)^5); \\ Michel Marcus, Nov 14 2015

CROSSREFS

Cf. A223023.

Sequence in context: A126527 A265842 A248884 * A122103 A009526 A304345

Adjacent sequences:  A223901 A223902 A223903 * A223905 A223906 A223907

KEYWORD

sign

AUTHOR

Takao Komatsu, Mar 29 2013

STATUS

approved

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Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)