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A208607 Triangle of coefficients of polynomials v(n,x) jointly generated with A208606; see the Formula section.

%I A208607 #5 Mar 30 2012 18:58:13
%S A208607 1,3,1,5,3,1,7,8,6,1,9,18,19,6,1,11,35,47,25,9,1,13,61,102,81,42,9,1,
%T A208607 15,98,203,219,147,51,12,1,17,148,378,520,435,216,74,12,1,19,213,666,
%U A208607 1122,1145,747,334,86,15,1,21,295,1119,2250,2753,2233,1245,450
%N A208607 Triangle of coefficients of polynomials v(n,x) jointly generated with A208606; see the Formula section.
%C A208607 Alternating rows sums: 1,2,3,4,5,6,7,8,...
%F A208607 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208607 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A208607 where u(1,x)=1, v(1,x)=1.
%e A208607 First five rows:
%e A208607 1
%e A208607 3...1
%e A208607 5...3...1
%e A208607 7...8...6...1
%e A208607 9...18...19...6...1
%e A208607 First five polynomials v(n,x):
%e A208607 1
%e A208607 3 + x
%e A208607 5 + 3x + x^2
%e A208607 7 + 8x + 6x^2 + x^3
%e A208607 9 + 18x + 19x^2 + 6x^3 + x^4
%t A208607 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208607 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208607 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A208607 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208607 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208607 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208607 TableForm[cu]
%t A208607 Flatten[%]  (* A208606 *)
%t A208607 Table[Expand[v[n, x]], {n, 1, z}]
%t A208607 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208607 TableForm[cv]
%t A208607 Flatten[%]  (* A208607 *)
%Y A208607 Cf. A208606.
%K A208607 nonn,tabl
%O A208607 1,2
%A A208607 _Clark Kimberling_, Feb 29 2012