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.

-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

Author

Roger L. Bagula and Gary W. Adamson, Jul 21 2008

Keywords

• tabl
• sign

Examples

			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;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A060821 (coefficients of Hermite polynomial).

Programs

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 *)

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

Formula

T(n, k) = H(n, k+1) - 2*H(n, k) - H(n, k-1), where H(n, k) = A060821(n+3, k).

Extensions

Name edited by G. C. Greubel, Dec 01 2020

Edited by G. C. Greubel, Apr 04 2021