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A207635 Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section.

%I A207635 #5 Mar 30 2012 18:58:13
%S A207635 1,2,5,2,11,9,2,23,29,13,2,47,81,55,17,2,95,209,191,89,21,2,191,513,
%T A207635 591,369,131,25,2,383,1217,1695,1329,631,181,29,2,767,2817,4607,4353,
%U A207635 2591,993,239,33,2,1535,6401,12031,13313,9535,4577,1471,305,37,2
%N A207635 Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section.
%F A207635 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207635 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A207635 where u(1,x)=1, v(1,x)=1.
%e A207635 First five rows:
%e A207635 1
%e A207635 2
%e A207635 5....2
%e A207635 11...9....2
%e A207635 23...29...13...2
%t A207635 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207635 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207635 v[n_, x_] := (x + 1)*u[n - 1, x]
%t A207635    + (x + 1)*v[n - 1, x] + 1
%t A207635 Table[Factor[u[n, x]], {n, 1, z}]
%t A207635 Table[Factor[v[n, x]], {n, 1, z}]
%t A207635 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207635 TableForm[cu]
%t A207635 Flatten[%]  (* A207635 *)
%t A207635 Table[Expand[v[n, x]], {n, 1, z}]
%t A207635 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207635 TableForm[cv]
%t A207635 Flatten[%]  (* A207636 *)
%Y A207635 Cf. A207636.
%K A207635 nonn,tabf
%O A207635 1,2
%A A207635 _Clark Kimberling_, Feb 24 2012