1,3

Row sums are:

{0, 2, 24, 80, 752, 2304, 25216, 77248, 1017216, 3152384, 48902144}

The results appear to be alternating orthogonal by the double integral

test using the Hermite weight function:

b = Table[Apply[Plus, Table[If[a[[n]][[i]] == 0, 0, x^(i - 1)*a1[[n]][[i]]/a[[n]][[i]]], {i, 1, Length[a[[n]]]}]], {n, 1, Length[a]}];

Table[Integrate[Exp[ -x^2/2]*b[[n]]*b[[m]], {x, -Infinity, Infinity}], {n, 1, Length[b]}, {m, 1, Length[b]}]

vector t(n)=2^n*n*If[ Coefficient[p[x,n]]<.0,ratio of coefficients of q(x,n)/p(x,n)]

{0},

{0, 2},

{16, 0, 8},

{0, 56, 0, 24},

{512, 0, 176, 0, 64},

{0, 1632, 0, 512, 0, 160},

{18432, 0, 4992, 0, 1408, 0, 384},

{0, 57984, 0, 14656, 0, 3712, 0, 896},

{786432, 0, 177792, 0, 41472, 0, 9472, 0, 2048},

{0, 2480640, 0, 529920, 0, 113664, 0, 23552, 0, 4608},

{39321600, 0, 7673856, 0, 1536000, 0, 303104, 0, 57344, 0, 10240}

Clear[P, x, n, a] (*Hermite-like*) P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - n*P[x, n - 2]; a1 = Table[CoefficientList[P[x, n], x], {n, 0, 10}]; (* Chebyshev-like*) Clear[B, x, n] B[x, 0] = 1; B[x, 1] = x; B[x_, n_] := B[x, n] = 2*x*B[x, n - 1] - B[x, n - 2]; a = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; (* converter*) b = Table[Table[If[a[[n]][[i]] == 0, 0, (n - 1)*2^(n - 1)* a1[[n]][[i]]/a[[n]][[i]]], {i, 1, Length[a[[n]]]}], {n, 1, Length[a]}]; Flatten[b]

Sequence in context: A135085 A080911 A056072 this_sequence A031361 A155955 A110709

Adjacent sequences: A136663 A136664 A136665 this_sequence A136667 A136668 A136669

nonn,uned,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 02 2008