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%I #5 Mar 30 2012 18:58:15
%S 1,2,3,2,6,7,3,10,17,15,3,16,39,46,31,4,21,69,129,119,63,4,30,112,260,
%T 386,296,127,5,36,172,492,890,1082,713,255,5,48,242,828,1898,2832,
%U 2897,1674,511,6,55,342,1318,3522,6682,8511,7495,3851,1023,6,70
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209581; see the Formula section.
%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)+2x*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 2...6....7
%e 3...10...17...15
%e 3...16...39...46...31
%e First three polynomials v(n,x): 1, 2 + 3x , 2 + 6x + 7x^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] + 2 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[%] (* A209581 *)
%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[%] (* A209582 *)
%Y Cf. A209581, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 11 2012
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