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

1,1

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];
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

Adjacent sequences: A140870 A140871 A140872 * A140874 A140875 A140876

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