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A140873
Triangle T(n, k) = H(n, k+1) - 2*H(n, k) - H(n, k-1), where H(n, k) = A060821(n+3, k), read by rows.
1
-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
OFFSET
1,1
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];
T[n_, k_]:= A060821[n+3, k+1] -2*A060821[n+3, k] -A060821[n+3, k-1];
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
def T(n, k): return A060821(n+3, k+1) -2*A060821(n+3, k) -A060821(n+3, k-1)
flatten([[T(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Apr 04 2021
CROSSREFS
Cf. A060821 (coefficients of Hermite polynomial).
Sequence in context: A075287 A277990 A103741 * A263225 A019285 A261970
KEYWORD
tabl,sign
AUTHOR
EXTENSIONS
Name edited by G. C. Greubel, Dec 01 2020
Edited by G. C. Greubel, Apr 04 2021
STATUS
approved