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A208932 Triangle of coefficients of polynomials v(n,x) jointly generated with A208932; see the Formula section.

%I A208932 #5 Mar 30 2012 18:58:14
%S A208932 1,3,2,5,8,4,7,22,24,8,9,48,84,60,16,11,90,228,264,148,32,13,152,528,
%T A208932 876,772,348,64,15,238,1092,2424,2992,2112,804,128,17,352,2072,5896,
%U A208932 9568,9392,5548,1820,256,19,498,3672,13008,26648,34080,27780
%N A208932 Triangle of coefficients of polynomials v(n,x) jointly generated with A208932; see the Formula section.
%C A208932 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A208932 For a discussion and guide to related arrays, see A208510.
%F A208932 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208932 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208932 where u(1,x)=1, v(1,x)=1.
%e A208932 First five rows:
%e A208932 1
%e A208932 3...2
%e A208932 5...8....4
%e A208932 7...22...24...8
%e A208932 9...48...84...60...16
%e A208932 First five polynomials v(n,x):
%e A208932 1
%e A208932 3 + 2x
%e A208932 5 + 8x + 4x^2
%e A208932 7 + 22x + 24x^2 + 8x^3
%e A208932 9 + 48x + 84x^2 + 60x^3 + 16x^4
%t A208932 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208932 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208932 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208932 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208932 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208932 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208932 TableForm[cu]
%t A208932 Flatten[%]    (* A208931 *)
%t A208932 Table[Expand[v[n, x]], {n, 1, z}]
%t A208932 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208932 TableForm[cv]
%t A208932 Flatten[%]    (* A208932 *)
%Y A208932 Cf. A208930, A208510.
%K A208932 nonn,tabl
%O A208932 1,2
%A A208932 _Clark Kimberling_, Mar 04 2012