OFFSET
1,1
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n, k) = H(n, k+1) - 2*H(n, k) - H(n, k-1), where H(n, k) = A060821(n+3, k).
EXAMPLE
Triangle begins as:
-60;
-240, -280;
840, -1440, -1200;
3360, 5040, -6720, -4704;
-15120, 26880, 26880, -26880, -17024;
-60480, -110880, 161280, 129024, -96768, -57600;
332640, -604800, -705600, 806400, 564480, -322560, -184320;
1330560, 2882880, -4435200, -3991680, 3548160, 2280960, -1013760, -563200;
MATHEMATICA
A060821[n_, k_]:= If[EvenQ[n-k], (-1)^(Floor[(n-k)/2])*(2^k)*n!/(k!*(Floor[(n - k)/2]!)), 0];
Table[T[n, k], {n, 15}, {k, n}]//Flatten (* corrected by G. C. Greubel, Dec 01 2020 *)
PROG
(Sage)
def A060821(n, k): return (-1)^((n-k)//2)*2^k*factorial(n)/(factorial(k)*factorial( (n-k)//2)) if (n-k)%2==0 else 0
flatten([[T(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Apr 04 2021
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula and Gary W. Adamson, Jul 21 2008
EXTENSIONS
Name edited by G. C. Greubel, Dec 01 2020
Edited by G. C. Greubel, Apr 04 2021
STATUS
approved