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A208612 Triangle of coefficients of polynomials u(n,x) jointly generated with A208613; see the Formula section.

%I A208612 #5 Mar 30 2012 18:58:13
%S A208612 1,1,1,1,4,2,1,9,9,3,1,16,26,19,5,1,25,60,70,38,8,1,36,120,197,167,73,
%T A208612 13,1,49,217,469,553,375,137,21,1,64,364,994,1528,1427,803,252,34,1,
%U A208612 81,576,1932,3714,4476,3449,1661,457,55,1,100,870,3510,8196
%N A208612 Triangle of coefficients of polynomials u(n,x) jointly generated with A208613; see the Formula section.
%F A208612 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208612 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208612 where u(1,x)=1, v(1,x)=1.
%e A208612 First five rows:
%e A208612 1
%e A208612 1...1
%e A208612 1...4....2
%e A208612 1...9....9....3
%e A208612 1...16...26...19...5
%e A208612 First five polynomials u(n,x):
%e A208612 1
%e A208612 1 + x
%e A208612 1 + 4x + 2x^2
%e A208612 1 + 9x + 9x^2 + 3x^3
%e A208612 1 + 16x + 26x^2 + 19x^3 + 5x^4
%t A208612 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208612 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208612 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208612 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208612 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208612 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208612 TableForm[cu]
%t A208612 Flatten[%]  (* A208612 *)
%t A208612 Table[Expand[v[n, x]], {n, 1, z}]
%t A208612 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208612 TableForm[cv]
%t A208612 Flatten[%]  (* A208613 *)
%Y A208612 Cf. A208613.
%K A208612 nonn,tabl
%O A208612 1,5
%A A208612 _Clark Kimberling_, Mar 01 2012