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A207633 Triangle of coefficients of polynomials u(n,x) jointly generated with A207634; see the Formula section.

%I A207633 #5 Mar 30 2012 18:58:13
%S A207633 1,2,4,3,7,9,6,12,22,21,12,20,48,62,48,24,33,98,157,163,108,48,54,192,
%T A207633 367,463,410,240,96,88,365,810,1203,1281,1000,528,192,143,679,1715,
%U A207633 2919,3634,3392,2384,1152,384,232,1242,3518,6742,9550,10379,8696
%N A207633 Triangle of coefficients of polynomials u(n,x) jointly generated with A207634; see the Formula section.
%F A207633 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207633 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A207633 where u(1,x)=1, v(1,x)=1.
%e A207633 First five rows:
%e A207633 1
%e A207633 2
%e A207633 4....3
%e A207633 7....9....6
%e A207633 12...22...21...12
%t A207633 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207633 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207633 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1
%t A207633 Table[Factor[u[n, x]], {n, 1, z}]
%t A207633 Table[Factor[v[n, x]], {n, 1, z}]
%t A207633 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207633 TableForm[cu]
%t A207633 Flatten[%]  (* A207633 *)
%t A207633 Table[Expand[v[n, x]], {n, 1, z}]
%t A207633 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207633 TableForm[cv]
%t A207633 Flatten[%]  (* A207634 *)
%Y A207633 Cf. A207634.
%K A207633 nonn,tabf
%O A207633 1,2
%A A207633 _Clark Kimberling_, Feb 24 2012