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A210861 Triangle of coefficients of polynomials v(n,x) jointly generated with A210860; see the Formula section.

%I A210861 #9 Dec 17 2012 15:43:03
%S A210861 1,2,2,6,7,3,16,30,20,5,50,116,108,47,8,156,460,552,338,105,13,532,
%T A210861 1842,2692,2119,941,221,21,1856,7532,13072,12574,7216,2452,451,34,
%U A210861 6876,31600,63240,71860,50525,22371,6035,895,55,26200,135576,308568
%N A210861 Triangle of coefficients of polynomials v(n,x) jointly generated with A210860; see the Formula section.
%C A210861 Row n ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A210861 Column 1:  A013989
%C A210861 Alternating row sums:  1,0,2,1,3,2,4,3,5,4,...
%C A210861 For a discussion and guide to related arrays, see A208510.
%F A210861 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A210861 v(n,x)=(x+n)*u(n-1,x)+x*v(n-1,x),
%F A210861 where u(1,x)=1, v(1,x)=1.
%e A210861 First five rows:
%e A210861 1
%e A210861 2....2
%e A210861 6....7.....3
%e A210861 16...30....20....5
%e A210861 50...116...108...47...8
%e A210861 First three polynomials v(n,x): 1, 2 + 2x, 6 + 7x + 3x^2
%t A210861 u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t A210861 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A210861 v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x];
%t A210861 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210861 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210861 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210861 TableForm[cu]
%t A210861 Flatten[%]   (* A210860 *)
%t A210861 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210861 TableForm[cv]
%t A210861 Flatten[%]   (* A210861 *)
%Y A210861 Cf. A210860, A208510.
%K A210861 nonn,tabl
%O A210861 1,2
%A A210861 _Clark Kimberling_, Mar 28 2012