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%I #5 Mar 30 2012 18:58:13
%S 1,2,4,3,7,9,6,12,22,21,12,20,48,62,48,24,33,98,157,163,108,48,54,192,
%T 367,463,410,240,96,88,365,810,1203,1281,1000,528,192,143,679,1715,
%U 2919,3634,3392,2384,1152,384,232,1242,3518,6742,9550,10379,8696
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A207634; 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)+2x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2
%e 4....3
%e 7....9....6
%e 12...22...21...12
%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] + 2 x*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[%] (* A207633 *)
%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[%] (* A207634 *)
%Y Cf. A207634.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Feb 24 2012
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