|
|
A224106
|
|
Numerators of poly-Cauchy numbers of the second kind hat c_n^(4).
|
|
3
|
|
|
1, -1, 97, -1147, 3472243, -653983, 74118189437, -1058923294571, 777910456216513, -285577840060819, 23240203016832136201, -216925341603548096639, 1222007019804929270080450811
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
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[Numerator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^4, {k, 0, n}]], {n, 0,
25}]
|
|
PROG
|
(PARI) a(n) = numerator(sum(k=0, n, (-1)^k*stirling(n, k, 1)/(k+1)^4)); \\ Michel Marcus, Nov 15 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|