0,5

Row sums are:

{1, 2, -2, -10, -3, 20, -4, -84, -5, 274, -6,...}.

p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal) Floor[n/2], (-1)^i*A109128[n, i], -(-1)^(n - i)* A109128[n, i]]], {i, 0, n}]/(1 - x);

t(n,m)=coefficients(p(x,n),x)

{1},

{1, 1},

{1, -4, 1},

{1, -6, -6, 1},

{1, -8, 11, -8, 1},

{1, -10, 19, 19, -10, 1},

{1, -12, 29, -40, 29, -12, 1},

{1, -14, 41, -70, -70, 41, -14, 1},

{1, -16, 55, -112, 139, -112, 55, -16, 1},

{1, -18, 71, -168, 251, 251, -168, 71, -18, 1},

{1, -20, 89, -240, 419, -504, 419, -240, 89, -20, 1}

Clear[A, p, n, i];

A[n_, 0] := 1;

A[n_, n_] := 1;

A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + 1;

p[x_, n_] = Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= Floor[n/2], (-1)^i*A[n, i], -(-1)^(n - i)*A[n, i]]], {i, 0, n}]/(1 - x);

Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 1, 11}];

Flatten[%]

A109128

Sequence in context: A084061 A140262 A049702 this_sequence A132046 A141540 A154326

Adjacent sequences: A159037 A159038 A159039 this_sequence A159041 A159042 A159043

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 03 2009