|
|
A112295
|
|
Inverse of a double factorial related triangle.
|
|
5
|
|
|
1, -1, 1, 0, -3, 1, 0, 0, -5, 1, 0, 0, 0, -7, 1, 0, 0, 0, 0, -9, 1, 0, 0, 0, 0, 0, -11, 1, 0, 0, 0, 0, 0, 0, -13, 1, 0, 0, 0, 0, 0, 0, 0, -15, 1, 0, 0, 0, 0, 0, 0, 0, 0, -17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Inverse of A112292. Similar results can be obtained for higher factorials.
|
|
LINKS
|
|
|
FORMULA
|
T(n, k) = 1 - 2*n if k = n-1 otherwise 0, with T(n, n) = 1.
Sum_{k=0..n} T(n, k) = 1 - 2*n - [n=0]. (End)
|
|
EXAMPLE
|
Triangle begins
1;
-1, 1;
0, -3, 1;
0, 0, -5, 1;
0, 0, 0, -7, 1;
0, 0, 0, 0, -9, 1;
0, 0, 0, 0, 0, -11, 1;
|
|
MATHEMATICA
|
T[n_, k_]:= If[k==n, 1, If[k==n-1, 1-2*n, 0]];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 17 2021 *)
|
|
PROG
|
(Sage)
def A112295(n, k): return 1 if k==n else 1-2*n if k==n-1 else 0
(Magma)
A112295:= func< n, k | k eq n select 1 else k eq n-1 select 1-2*n else 0 >;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|