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A207618 Triangle of coefficients of polynomials u(n,x) jointly generated with A207619; see the Formula section.

%I A207618 #5 Mar 30 2012 18:58:13
%S A207618 1,2,3,3,4,7,6,5,12,17,12,6,18,34,40,24,7,25,58,91,92,48,8,33,90,173,
%T A207618 234,208,96,9,42,131,295,489,584,464,192,10,52,182,467,906,1328,1424,
%U A207618 1024,384,11,63,244,700,1545,2651,3496,3408,2240,768,12,75,318
%N A207618 Triangle of coefficients of polynomials u(n,x) jointly generated with A207619; see the Formula section.
%F A207618 u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
%F A207618 where u(1,x)=1, v(1,x)=1.
%e A207618 First five rows:
%e A207618 1
%e A207618 2
%e A207618 3...3
%e A207618 4...7....6
%e A207618 5...12...17...12
%t A207618 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207618 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207618 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1
%t A207618 Table[Factor[u[n, x]], {n, 1, z}]
%t A207618 Table[Factor[v[n, x]], {n, 1, z}]
%t A207618 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207618 TableForm[cu]
%t A207618 Flatten[%]    (* A207618 *)
%t A207618 Table[Expand[v[n, x]], {n, 1, z}]
%t A207618 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207618 TableForm[cv]
%t A207618 Flatten[%]    (* A207619 *)
%Y A207618 Cf. A207619.
%K A207618 nonn,tabf
%O A207618 1,2
%A A207618 _Clark Kimberling_, Feb 20 2012