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A210800 Triangle of coefficients of polynomials v(n,x) jointly generated with A210799; see the Formula section.

%I A210800 #10 Sep 08 2013 19:59:33
%S A210800 1,1,2,5,4,3,5,14,9,5,17,28,36,19,8,17,70,88,83,38,13,53,136,251,245,
%T A210800 181,73,21,53,298,557,746,613,379,137,34,161,568,1376,1930,2030,1439,
%U A210800 769,252,55,161,1162,2888,5026,5818,5139,3221,1524,457,89,485
%N A210800 Triangle of coefficients of polynomials v(n,x) jointly generated with A210799; see the Formula section.
%C A210800 Row n starts a term of A048473 and ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A210800 Alternating row sums: 1,2,3,4,5,6,7,...
%C A210800 For a discussion and guide to related arrays, see A208510.
%F A210800 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A210800 v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x),
%F A210800 where u(1,x)=1, v(1,x)=1.
%F A210800 T(n,k) = T(n-1,k-1) + 3*T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2) + a(k) with a(0) = 2, a(1) = 1, a(k) = 0 if k>1, T(1,0) = T(2,0) = 1, T(2,1) = 2 and T(n,k) = 0 if k<0 or if k >n. - _Philippe Deléham_, Mar 31 2012
%e A210800 First five rows:
%e A210800 1
%e A210800 1....2
%e A210800 5....4....3
%e A210800 5....14...9....5
%e A210800 17...28...36...19...8
%e A210800 First three polynomials v(n,x): 1, 1 + 2x, 5 + 4x + 3x^2
%t A210800 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210800 u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
%t A210800 d[x_] := h + x; e[x_] := p + x;
%t A210800 v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
%t A210800 j = 1; c = 1; h = 2; p = -1; f = 0;
%t A210800 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210800 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210800 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210800 TableForm[cu]
%t A210800 Flatten[%]   (* A210799 *)
%t A210800 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210800 TableForm[cv]
%t A210800 Flatten[%]   (* A210800 *)
%Y A210800 Cf. A210799, A208510.
%K A210800 nonn,tabl
%O A210800 1,3
%A A210800 _Clark Kimberling_, Mar 27 2012