|
|
A222636
|
|
Poly-Cauchy numbers c_n^(-3).
|
|
4
|
|
|
1, 8, 19, -1, -10, 48, -234, 1302, -8328, 60672, -497688, 4547448, -45846864, 505862064, -6065584128, 78555965184, -1093053332736, 16264215348480, -257730606190080, 4333624828853760, -77067187081620480, 1445257352902763520, -28505367984508416000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Definition of poly-Cauchy numbers in A222627.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} Stirling1(n,k)*(k+1)^3.
E.g.f.: (1 + x) * (1 + 7 * log(1 + x) + 6 * log(1 + x)^2 + log(1 + x)^3). - Ilya Gutkovskiy, Aug 10 2021
|
|
MATHEMATICA
|
Table[Sum[StirlingS1[n, k] (k + 1)^3, {k, 0, n}], {n, 0, 25}]
|
|
PROG
|
(Magma) [&+[StirlingFirst(n, k)*(k+1)^3: k in [0..n]]: n in [0..25]]; // Bruno Berselli, Mar 28 2013
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*(k+1)^3); \\ Michel Marcus, Nov 14 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|