1,3

Row sums:

{1, 2, 12, 28, 192, 496, 4320, 12000, 130688, 381696, 5015040};

Suppose that you have an

Chebyshev-like recursion: ( one type)

P[x,n]=x*P[x,n-1]-P[x,n-2]

and an Hermite:

Q[x,n]=x*Q[x,n-1]-n*Q[x,n-2]

You can define a set of Matrices on the Coefficent list vectors:

vp[n]=M[n].vq[n]

vq[n].vq[n]t=delta[i,j]

vp[n].vq[n]t=M[n]

Where M[n] is a diagonal matrix( a vector)

Then a new set of polynomials made!

T(n,m)=If[A137286(m)>0,A049310(n)/A137286(m),0] Out_vector=2^(n-1)*T(n,m)

{1},

{0, 2},

{8, 0, 4},

{0, 20, 0, 8},

{128, 0, 48, 0, 16},

{0, 352, 0, 112, 0, 32},

{3072, 0, 928, 0, 256, 0, 64},

{0, 8928, 0, 2368, 0, 576, 0, 128},

{98304, 0, 24960, 0, 5888, 0, 1280, 0, 256},

{0, 296448, 0, 67584, 0, 14336, 0, 2816, 0, 512},

{3932160, 0, 863232, 0, 178176, 0, 34304, 0, 6144, 0, 1024}

Clear[P, x, n, a] (*Hermite : A137286*) P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = x*P[x, n - 1] - n*P[x, n - 2]; a1 = Table[CoefficientList[P[x, n], x], {n, 0, 10}]; (* Chebyshev : other kind : A049310*) Clear[B, x, n] B[x, 0] = 1; B[x, 1] = x; B[x_, n_] := B[x, n] = 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, 2^(n - 1)*a1[[n]][[i]]/a[[n]][[i]]], {i, 1, Length[a[[n]]]}], {n, 1, Length[a]}]; Flatten[b]

Cf. A137286, A049310.

Sequence in context: A016593 A020818 A021785 this_sequence A086728 A118292 A011055

Adjacent sequences: A136661 A136662 A136663 this_sequence A136665 A136666 A136667

nonn,uned,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 01 2008