A140874 - OEIS

%I #5 Sep 09 2013 19:24:57

%S -4,-4,-8,-3,-12,-13,-1,-15,-25,-19,2,-16,-40,-44,-26,6,-14,-56,-84,

%T -70,-34,11,-8,-70,-140,-154,-104,-43,17,3,-78,-210,-294,-258,-147,

%U -53,24,20,-75,-288,-504,-552,-405,-200,-64

%N Triangle T(n,k) = binomial(n,k+2)-2*binomial(n,k+1)-binomial(n,k) read by rows, 0<=k<=n-2, n>=2.

%C Row sums are 4-2^(n+1).

%e -4;

%e -4, -8;

%e -3, -12, -13;

%e -1, -15, -25, -19;

%e 2, -16, -40, -44, -26;

%e 6, -14, -56, -84, -70, -34;

%e 11, -8, -70, -140, -154, -104, -43;

%e 17, 3, -78, -210, -294, -258, -147, -53;

%e 24, 20, -75, -288, -504, -552, -405, -200, -64;

%t Clear[T, D2, x, a, n, m] T[n_, m_] := Binomial[n, m] D2[n_, m_] := If[m + 2 <= n, T[n, m + 2] - 2*T[n, m + 1] - T[n, m], {} ]; a = Table[Flatten[Table[D2[n, m], {m, 0, n}]], {n, 0, 10}]; Flatten[a]

%Y Cf. A007318.

%K easy,tabl,sign

%O 2,1

%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 21 2008

%E Sign in definition corrected by _R. J. Mathar_, Sep 09 2013