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 A207635 Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section. 3

%I

%S 1,2,5,2,11,9,2,23,29,13,2,47,81,55,17,2,95,209,191,89,21,2,191,513,

%T 591,369,131,25,2,383,1217,1695,1329,631,181,29,2,767,2817,4607,4353,

%U 2591,993,239,33,2,1535,6401,12031,13313,9535,4577,1471,305,37,2

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section.

%F u(n,x)=u(n-1,x)+v(n-1,x),

%F v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 2

%e 5....2

%e 11...9....2

%e 23...29...13...2

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := u[n - 1, x] + v[n - 1, x]

%t v[n_, x_] := (x + 1)*u[n - 1, x]

%t + (x + 1)*v[n - 1, x] + 1

%t Table[Factor[u[n, x]], {n, 1, z}]

%t Table[Factor[v[n, x]], {n, 1, z}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A207635 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%] (* A207636 *)

%Y Cf. A207636.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Feb 24 2012

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