|
|
A329819
|
|
Triangular array, read by rows: T(n,k) = [(x*y*z)^k] (-1 + (1 + x + 1/x)*(1 + y + 1/y)*(1 + z + 1/z))^n for -n <= k <= n.
|
|
3
|
|
|
1, 1, 0, 1, 1, 6, 26, 6, 1, 1, 24, 195, 264, 195, 24, 1, 1, 60, 898, 3276, 5646, 3276, 898, 60, 1, 1, 120, 3065, 22260, 72730, 101520, 72730, 22260, 3065, 120, 1, 1, 210, 8526, 105690, 581475, 1510860, 2103740, 1510860, 581475, 105690, 8526, 210, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = T(n,-k).
|
|
EXAMPLE
|
Triangle begins:
1;
1, 0, 1;
1, 6, 26, 6, 1;
1, 24, 195, 264, 195, 24, 1;
1, 60, 898, 3276, 5646, 3276, 898, 60, 1;
1, 120, 3065, 22260, 72730, 101520, 72730, 22260, 3065, 120, 1;
|
|
PROG
|
(PARI) {T(n, k) = polcoef(polcoef(polcoef((-1+(1+x+1/x)*(1+y+1/y)*(1+z+1/z))^n, k), k), k)}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|