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A207630 Triangle of coefficients of polynomials v(n,x) jointly generated with A207629; see the Formula section.

%I A207630 #5 Mar 30 2012 18:58:13
%S A207630 1,3,1,6,3,12,9,1,24,24,5,48,60,19,1,96,144,62,7,192,336,184,33,1,384,
%T A207630 768,512,128,9,768,1728,1360,440,51,1,1536,3840,3488,1392,230,11,3072,
%U A207630 8448,8704,4144,900,73,1,6144,18432,21248,11776,3192,376,13
%N A207630 Triangle of coefficients of polynomials v(n,x) jointly generated with A207629; see the Formula section.
%F A207630 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207630 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A207630 where u(1,x)=1, v(1,x)=1.
%e A207630 First five rows:
%e A207630 1
%e A207630 3....1
%e A207630 6....3
%e A207630 12...9....1
%e A207630 24...24...5
%t A207630 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207630 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207630 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1
%t A207630 Table[Factor[u[n, x]], {n, 1, z}]
%t A207630 Table[Factor[v[n, x]], {n, 1, z}]
%t A207630 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207630 TableForm[cu]
%t A207630 Flatten[%]  (* A207629 *)
%t A207630 Table[Expand[v[n, x]], {n, 1, z}]
%t A207630 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207630 TableForm[cv]
%t A207630 Flatten[%]  (* A207630 *)
%Y A207630 Cf. A207629.
%K A207630 nonn,tabf
%O A207630 1,2
%A A207630 _Clark Kimberling_, Feb 23 2012