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

%I A208606 #9 Sep 03 2021 13:58:02
%S A208606 1,1,1,1,4,1,1,9,4,1,1,16,12,7,1,1,25,30,26,7,1,1,36,65,73,32,10,1,1,
%T A208606 49,126,175,113,52,10,1,1,64,224,378,332,199,61,13,1,1,81,372,756,852,
%U A208606 634,277,87,13,1,1,100,585,1422,1974,1779,1024,421,99,16,1,1,121
%N A208606 Triangle of coefficients of polynomials u(n,x) jointly generated with A208607; see the Formula section.
%F A208606 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208606 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A208606 where u(1,x)=1, v(1,x)=1.
%e A208606 First five rows:
%e A208606 1
%e A208606 1...1
%e A208606 1...4....1
%e A208606 1...9....4....1
%e A208606 1...16...12...7...1
%e A208606 First five polynomials u(n,x):
%e A208606 1
%e A208606 1 + x
%e A208606 1 + 4x + 1x^2
%e A208606 1 + 9x + 4x^2 + x^3
%e A208606 1 + 16x + 12x^2 + 7x^3 + x^4
%t A208606 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208606 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208606 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A208606 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208606 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208606 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208606 TableForm[cu]
%t A208606 Flatten[%]  (* A208606 *)
%t A208606 Table[Expand[v[n, x]], {n, 1, z}]
%t A208606 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208606 TableForm[cv]
%t A208606 Flatten[%]  (* A208607 *)
%Y A208606 Cf. A208607.
%K A208606 nonn,tabl
%O A208606 1,5
%A A208606 _Clark Kimberling_, Feb 29 2012
%E A208606 a(68) corrected by _Georg Fischer_, Sep 03 2021