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A209152 Triangle of coefficients of polynomials u(n,x) jointly generated with A208339; see the Formula section.

%I A209152 #5 Mar 30 2012 18:58:15
%S A209152 1,2,1,3,5,3,4,10,14,7,5,16,32,37,17,6,23,58,97,98,41,7,31,93,197,287,
%T A209152 257,99,8,40,138,348,642,830,670,239,9,50,194,562,1234,2024,2360,1737,
%U A209152 577,10,61,262,852,2148,4198,6220,6617,4482,1393,11,73,343
%N A209152 Triangle of coefficients of polynomials u(n,x) jointly generated with A208339; see the Formula section.
%C A209152 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209152 For a discussion and guide to related arrays, see A208510.
%F A209152 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209152 v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
%F A209152 where u(1,x)=1, v(1,x)=1.
%e A209152 First five rows:
%e A209152 1
%e A209152 2...1
%e A209152 3...5....3
%e A209152 4...10...14...7
%e A209152 5...16...32...37...17
%e A209152 First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 3x^2.
%t A209152 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209152 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209152 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209152 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209152 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209152 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209152 TableForm[cu]
%t A209152 Flatten[%]    (* A209152 *)
%t A209152 Table[Expand[v[n, x]], {n, 1, z}]
%t A209152 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209152 TableForm[cv]
%t A209152 Flatten[%]    (* A208339 *)
%Y A209152 Cf. A208339, A208510.
%K A209152 nonn,tabl
%O A209152 1,2
%A A209152 _Clark Kimberling_, Mar 07 2012