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 A159040 A triangle of polynomial coefficients: 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). 0

%I

%S 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,

%T 29,-12,1,1,-14,41,-70,-70,41,-14,1,1,-16,55,-112,139,-112,55,-16,1,1,

%U -18,71,-168,251,251,-168,71,-18,1,1,-20,89,-240,419,-504,419,-240,89,-20,1

%N A triangle of polynomial coefficients: 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).

%C Row sums are:

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

%F 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);

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

%e {1},

%e {1, 1},

%e {1, -4, 1},

%e {1, -6, -6, 1},

%e {1, -8, 11, -8, 1},

%e {1, -10, 19, 19, -10, 1},

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

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

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

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

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

%t Clear[A, p, n, i];

%t A[n_, 0] := 1;

%t A[n_, n_] := 1;

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

%t 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);

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

%t Flatten[%]

%Y A109128

%K sign,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Apr 03 2009

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)