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A208912 Triangle of coefficients of polynomials v(n,x) jointly generated with A208911; see the Formula section.

%I A208912 #5 Mar 30 2012 18:58:14
%S A208912 1,2,2,3,5,4,4,9,15,8,5,14,36,37,16,6,20,70,105,91,32,7,27,120,235,
%T A208912 306,213,64,8,35,189,455,791,819,491,128,9,44,280,798,1736,2380,2136,
%U A208912 1109,256,10,54,396,1302,3402,5796,6924,5373,2475,512,11,65,540
%N A208912 Triangle of coefficients of polynomials v(n,x) jointly generated with A208911; see the Formula section.
%C A208912 For a discussion and guide to related arrays, see A208510.
%F A208912 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208912 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208912 where u(1,x)=1, v(1,x)=1.
%e A208912 First five rows:
%e A208912 1
%e A208912 2...2
%e A208912 3...5....3
%e A208912 4...9....15...8
%e A208912 5...14...36...37...16
%e A208912 First five polynomials v(n,x):
%e A208912 1
%e A208912 2 + 2x
%e A208912 3 + 5x + 3x^2
%e A208912 4 + 9x + 15x^2 + 8x^3
%e A208912 5 + 14x + 36x^2 + 37x^3 + 16x^4
%t A208912 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208912 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208912 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208912 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208912 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208912 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208912 TableForm[cu]
%t A208912 Flatten[%]    (* A208911 *)
%t A208912 Table[Expand[v[n, x]], {n, 1, z}]
%t A208912 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208912 TableForm[cv]
%t A208912 Flatten[%]    (* A208912 *)
%Y A208912 Cf. A208911, A208510.
%K A208912 nonn,tabl
%O A208912 1,2
%A A208912 _Clark Kimberling_, Mar 03 2012