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

%I A210860 #18 Jan 12 2022 09:30:50
%S A210860 1,2,1,4,5,2,10,18,12,3,26,64,62,28,5,76,230,286,183,60,8,232,846,
%T A210860 1298,1073,503,126,13,764,3220,5832,5884,3563,1288,255,21,2620,12608,
%U A210860 26436,31530,23353,10956,3158,506,34,9496,51084,121276,166630
%N A210860 Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.
%C A210860 Row n ends with F(n), where F=A000045 (Fibonacci numbers).
%C A210860 Column 1:  A000085
%C A210860 For a discussion and guide to related arrays, see A208510.
%F A210860 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A210860 v(n,x)=(x+n)*u(n-1,x)+x*v(n-1,x),
%F A210860 where u(1,x)=1, v(1,x)=1.
%e A210860 First five rows:
%e A210860    1
%e A210860    2    1
%e A210860    4    5    2
%e A210860   10   18   12    3
%e A210860   26   64   62   28    5
%e A210860 First three polynomials u(n,x): 1, 2 + x, 4 + 5x + 2x^2.
%t A210860 u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t A210860 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A210860 v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x];
%t A210860 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210860 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210860 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210860 TableForm[cu]
%t A210860 Flatten[%]   (* A210860 *)
%t A210860 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210860 TableForm[cv]
%t A210860 Flatten[%]   (* A210861 *)
%Y A210860 Cf. A210861, A208510.
%K A210860 nonn,tabl
%O A210860 1,2
%A A210860 _Clark Kimberling_, Mar 28 2012
%E A210860 Definition clarified by _Alonso del Arte_ and _Harvey P. Dale_, Dec 17 2012