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%I #7 Mar 30 2012 18:58:13
%S 1,2,3,3,9,3,4,20,18,3,5,38,62,27,3,6,65,164,131,36,3,7,103,369,461,
%T 227,45,3,8,154,742,1324,1010,350,54,3,9,220,1372,3298,3578,1892,500,
%U 63,3,10,303,2376,7386,10768,8022,3188,677,72,3,11,405,3903,15222
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207625; see the Formula section.
%F u(n,x)=u(n-1,x)+v(n-1,x),
%F v(n,x)=2x*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...3
%e 3...9...3
%e 4...20...18...3
%e 5...38...62...27...3
%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_] := 2 x*u[n - 1, x] + (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[%] (* A207625 *)
%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[%] (* A207626 *)
%Y Cf. A207625.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Feb 21 2012
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