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A209775 Triangle of coefficients of polynomials u(n,x) jointly generated with A209776; see the Formula section.

%I A209775 #5 Mar 30 2012 18:58:15
%S A209775 1,1,2,3,6,4,5,16,18,8,9,36,60,48,16,15,76,166,194,120,32,25,152,414,
%T A209775 634,572,288,64,41,294,960,1822,2154,1584,672,128,67,554,2114,4790,
%U A209775 7004,6752,4192,1536,256,109,1024,4476,11800,20560,24498,19952
%N A209775 Triangle of coefficients of polynomials u(n,x) jointly generated with A209776; see the Formula section.
%C A209775 For a discussion and guide to related arrays, see A208510.
%F A209775 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209775 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209775 where u(1,x)=1, v(1,x)=1.
%e A209775 First five rows:
%e A209775 1
%e A209775 1...2
%e A209775 3...6....4
%e A209775 5...16...18...8
%e A209775 9...36...60...48...16
%e A209775 First three polynomials u(n,x): 1, 1 + 2x, 3 + 6x + 4x^2.
%t A209775 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209775 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209775 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209775 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209775 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209775 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209775 TableForm[cu]
%t A209775 Flatten[%]    (* A209775 *)
%t A209775 Table[Expand[v[n, x]], {n, 1, z}]
%t A209775 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209775 TableForm[cv]
%t A209775 Flatten[%]    (* A209776 *)
%Y A209775 Cf. A209776, A208510.
%K A209775 nonn,tabl
%O A209775 1,3
%A A209775 _Clark Kimberling_, Mar 15 2012