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%I #5 Mar 30 2012 18:58:15
%S 1,3,2,5,7,3,9,18,14,4,15,42,48,25,5,25,89,137,107,41,6,41,180,348,
%T 364,212,63,7,67,350,820,1078,844,386,92,8,109,663,1827,2902,2864,
%U 1773,659,129,9,177,1230,3906,7284,8692,6809,3453,1069,175,10,287
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209583; see the Formula section.
%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%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)+(x+1)
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 3....1
%e 5....7....3
%e 9....18...14...4
%e 15...42...48...25...5
%e First three polynomials v(n,x): 1, 3 + x , 5 + 7x + 3x^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] + (x + 1)*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[%] (* A209583 *)
%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[%] (* A209584 *)
%Y Cf. A209583, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 11 2012
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