|
|
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
(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
|
|
|
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
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|