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A207626 Triangle of coefficients of polynomials v(n,x) jointly generated with A207625; see the Formula section.

%I A207626 #7 Mar 30 2012 18:58:13
%S A207626 1,2,3,3,9,3,4,20,18,3,5,38,62,27,3,6,65,164,131,36,3,7,103,369,461,
%T A207626 227,45,3,8,154,742,1324,1010,350,54,3,9,220,1372,3298,3578,1892,500,
%U A207626 63,3,10,303,2376,7386,10768,8022,3188,677,72,3,11,405,3903,15222
%N A207626 Triangle of coefficients of polynomials v(n,x) jointly generated with A207625; see the Formula section.
%F A207626 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207626 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A207626 where u(1,x)=1, v(1,x)=1.
%e A207626 First five rows:
%e A207626 1
%e A207626 2...3
%e A207626 3...9...3
%e A207626 4...20...18...3
%e A207626 5...38...62...27...3
%t A207626 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207626 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207626 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
%t A207626 Table[Factor[u[n, x]], {n, 1, z}]
%t A207626 Table[Factor[v[n, x]], {n, 1, z}]
%t A207626 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207626 TableForm[cu]
%t A207626 Flatten[%]    (* A207625 *)
%t A207626 Table[Expand[v[n, x]], {n, 1, z}]
%t A207626 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207626 TableForm[cv]
%t A207626 Flatten[%]    (* A207626 *)
%Y A207626 Cf. A207625.
%K A207626 nonn,tabl
%O A207626 1,2
%A A207626 _Clark Kimberling_, Feb 21 2012