OFFSET
0,5
COMMENTS
LINKS
G. C. Greubel, Rows n=0..100 of triangle, flattened
FORMULA
T(n, k) = (-1)^(n-k)*(n-k)!*C(1+[n/2], k+1-[(n+1)/2])*C([(n+1)/2], k-[n/2]).
EXAMPLE
Rows begin:
1;
-1,1;
0,-2,1;
0,2,-4,1;
0,0,6,-6,1;
0,0,-6,18,-9,1;
0,0,0,-24,36,-12,1;
0,0,0,24,-96,72,-16,1;
0,0,0,0,120,-240,120,-20,1;
0,0,0,0,-120,600,-600,200,-25,1;
...
Unsigned columns read downwards equals rows of matrix inverse A104557 read backwards:
1;
1,1;
2,2,1;
6,6,4,1;
24,24,18,6,1;
120,120,96,36,9,1;
...
MATHEMATICA
T[n_, k_] := (-1)^(n - k)*(n - k)!*Binomial[1 + Floor[n/2], k + 1 - Floor[(n + 1)/2]]*Binomial[Floor[(n+1)/2], k -Floor[n/2]]; Table[T[n, k], {n, 0, 20}, {k, 0, n}]//Flatten (* G. C. Greubel, May 14 2018 *)
PROG
(PARI) {T(n, k)=(-1)^(n-k)*(n-k)!*binomial(1+n\2, k+1-(n+1)\2)* binomial( (n+1)\2, k-n\2)};
(Magma) /* As triangle */ [[(-1)^(n-k)*Factorial(n-k)*Binomial(1+ Floor(n/2), k +1 -Floor((n+1)/2))*Binomial(Floor((n+1)/2), k - Floor(n/2)): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 14 2018
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Mar 16 2005
STATUS
approved