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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.

%I A140873 #21 Apr 05 2021 00:06:16
%S A140873 -60,-240,-280,840,-1440,-1200,3360,5040,-6720,-4704,-15120,26880,
%T A140873 26880,-26880,-17024,-60480,-110880,161280,129024,-96768,-57600,
%U A140873 332640,-604800,-705600,806400,564480,-322560,-184320,1330560,2882880,-4435200,-3991680,3548160,2280960,-1013760,-563200
%N 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.
%H A140873 G. C. Greubel, <a href="/A140873/b140873.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A140873 T(n, k) =  H(n, k+1) - 2*H(n, k) - H(n, k-1), where H(n, k) = A060821(n+3, k).
%e A140873 Triangle begins as:
%e A140873       -60;
%e A140873      -240,    -280;
%e A140873       840,   -1440,    -1200;
%e A140873      3360,    5040,    -6720,    -4704;
%e A140873    -15120,   26880,    26880,   -26880,  -17024;
%e A140873    -60480, -110880,   161280,   129024,  -96768,  -57600;
%e A140873    332640, -604800,  -705600,   806400,  564480, -322560,  -184320;
%e A140873   1330560, 2882880, -4435200, -3991680, 3548160, 2280960, -1013760, -563200;
%t A140873 A060821[n_, k_]:= If[EvenQ[n-k], (-1)^(Floor[(n-k)/2])*(2^k)*n!/(k!*(Floor[(n - k)/2]!)), 0];
%t A140873 T[n_, k_]:= A060821[n+3, k+1] -2*A060821[n+3, k] -A060821[n+3, k-1];
%t A140873 Table[T[n, k], {n, 15}, {k, n}]//Flatten (* corrected by _G. C. Greubel_, Dec 01 2020 *)
%o A140873 (Sage)
%o A140873 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
%o A140873 def T(n,k): return A060821(n+3, k+1) -2*A060821(n+3, k) -A060821(n+3, k-1)
%o A140873 flatten([[T(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Apr 04 2021
%Y A140873 Cf. A060821 (coefficients of Hermite polynomial).
%K A140873 tabl,sign
%O A140873 1,1
%A A140873 _Roger L. Bagula_ and _Gary W. Adamson_, Jul 21 2008
%E A140873 Name edited by _G. C. Greubel_, Dec 01 2020
%E A140873 Edited by _G. C. Greubel_, Apr 04 2021