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%I #7 Mar 30 2012 18:58:15
%S 1,3,1,5,3,1,9,8,4,1,15,19,13,5,1,25,41,36,19,6,1,41,84,90,60,26,7,1,
%T 67,165,210,169,92,34,8,1,109,315,465,439,287,133,43,9,1,177,588,990,
%U 1073,818,454,184,53,10,1,287,1079,2043,2502,2178,1405,681,246
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209577; see the Formula section.
%C Alternating row sums: 1,0,2,1,3,2,4,3,5,4,... (A028242).
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...1
%e 3...2....1
%e 5...6....3....1
%e 9...13...10...4...1
%e First three polynomials v(n,x): 1, 1 + x , 3 + 2x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A209577 *)
%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[%] (* A209578 *)
%Y Cf. A209577, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 11 2012
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