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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
From G. C. Greubel, Feb 17 2021: (Start)
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
flatten([[A112295(n, k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Feb 17 2021
(Magma)
A112295:= func< n, k | k eq n select 1 else k eq n-1 select 1-2*n else 0 >;
[A112295(n, k): k in [0..n], n in [0..15]]; // G. C. Greubel, Feb 17 2021
CROSSREFS
Sequence in context: A058865 A318502 A115090 * A318973 A110517 A091925
KEYWORD
sign,tabl
AUTHOR
Paul Barry, Sep 01 2005
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)