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A208611 Triangle of coefficients of polynomials v(n,x) jointly generated with A208610; see the Formula section.

%I A208611 #5 Mar 30 2012 18:58:13
%S A208611 1,2,3,2,6,7,2,8,18,17,2,10,30,52,41,2,12,44,102,146,99,2,14,60,170,
%T A208611 328,402,239,2,16,78,258,610,1014,1090,577,2,18,98,368,1016,2076,3044,
%U A208611 2920,1393,2,20,120,502,1572,3756,6792,8932,7746,3363,2,22,144
%N A208611 Triangle of coefficients of polynomials v(n,x) jointly generated with A208610; see the Formula section.
%F A208611 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208611 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A208611 where u(1,x)=1, v(1,x)=1.
%e A208611 First five rows:
%e A208611 1
%e A208611 2...3
%e A208611 2...6....7
%e A208611 2...8....18...17
%e A208611 2...10...30...52...41
%e A208611 First five polynomials v(n,x):
%e A208611 1
%e A208611 2 + 3x
%e A208611 2 + 6x + 7x^2
%e A208611 2 + 8x + 18x^2 + 17x^3
%e A208611 2 + 10x + 30x^2 + 52x^3 + 41x^4
%t A208611 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208611 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208611 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208611 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208611 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208611 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208611 TableForm[cu]
%t A208611 Flatten[%]  (* A208610 *)
%t A208611 Table[Expand[v[n, x]], {n, 1, z}]
%t A208611 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208611 TableForm[cv]
%t A208611 Flatten[%]  (* A208611 *)
%Y A208611 Cf. A208610.
%K A208611 nonn,tabl
%O A208611 1,2
%A A208611 _Clark Kimberling_, Mar 01 2012