1,3

Row sums are:

Table[Apply[Plus, CoefficientList[P[x, n], x]], {n, 0, 10}]

{1, 2, 4, 4, -1, -8, -9, 0, 12, 14, 1}

Double Integrations are alternating:

Table[Table[Integrate[Sqrt[1/(1 - x^2)]*P[x,n]*P[x, m], {x, -1, 1}], {n, 0, 10}], {m, 0, 10}]

Karem Boubaker, On modified Boubaker polynomials..., Trends in Appl. Sci. Research, 2 (2007), 540-544.

Karem Boubaker et al., Enhancement of pyrolysis spray disposal performance ..., Eur. Phys. J. Appl. Phys., 37 (2007), 105-109. [Link requires a subscription]

Hedi Labiadh and Karem Boubaker, A Sturm-Liouville shaped characteristic differential equation ..., Differential Equations and Control Processes, No. 2 (2007).

Defferentiation of recursive polynomials: B(x, n) = x*B(x, n - 1) - B(x, n - 2); P(x,n)=dB(x,n+1)/dx

{1},

{0, 2},

{1, 0, 3},

{0, 0, 0, 4},

{-3, 0, -3, 0, 5},

{0, -6, 0, -8, 0, 6},

{5, 0, -6, 0, -15, 0, 7},

{0, 16, 0, 0, 0, -24, 0, 8},

{-7, 0, 30, 0, 15, 0, -35, 0, 9},

{0, -30, 0, 40, 0,42, 0, -48, 0, 10},

{9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11}

Clear[B, x, n] B[x, 0] = 1; B[x, 1] = x; B[x, 2] = 2 + x^2; B[x, 3] = x + x^3; B[x, 4] = -2 + x^4; B[x_, n_] := B[x, n] = x*B[x, n - 1] - B[x, n - 2] P[x_, n_] := D[B[x, n + 1], x] Table[ExpandAll[P[x, n]], {n, 0, 10}] a = Table[CoefficientList[P[x, n], x], {n, 0, 10}] Flatten[a]

Cf. A138034, A135929, A135936, A137276, A137277, A137289.

Sequence in context: A059084 A070677 A029584 this_sequence A127373 A050464 A014405

Adjacent sequences: A136252 A136253 A136254 this_sequence A136256 A136257 A136258

nonn,uned,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 17 2008