# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a210862 Showing 1-1 of 1 %I A210862 #5 Mar 30 2012 18:58:17 %S A210862 1,2,1,3,2,2,4,6,7,3,5,15,20,16,5,6,31,57,63,37,8,7,56,153,215,184,81, %T A210862 13,8,92,370,684,771,513,171,21,9,141,805,2028,2898,2603,1354,351,34, %U A210862 10,205,1598,5515,10084,11582,8319,3415,703,55,11,286,2940 %N A210862 Triangle of coefficients of polynomials u(n,x) jointly generated with A210863; see the Formula section. %C A210862 Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers). %C A210862 Column 2: A056520 %C A210862 For a discussion and guide to related arrays, see A208510. %F A210862 u(n,x)=u(n-1,x)+x*v(n-1,x)+1, %F A210862 v(n,x)=(x+n-1)*u(n-1,x)+x*v(n-1,x), %F A210862 where u(1,x)=1, v(1,x)=1. %e A210862 First five rows: %e A210862 1 %e A210862 2...1 %e A210862 3...2....2 %e A210862 4...6....7....3 %e A210862 5...15...20...16...5 %e A210862 First three polynomials u(n,x): 1, 2 + x, 4 + 5x + 2x^2. %t A210862 u[1, x_] := 1; v[1, x_] := 1; z = 14; %t A210862 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1; %t A210862 v[n_, x_] := (x + n - 1)*u[n - 1, x] + x*v[n - 1, x]; %t A210862 Table[Expand[u[n, x]], {n, 1, z/2}] %t A210862 Table[Expand[v[n, x]], {n, 1, z/2}] %t A210862 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; %t A210862 TableForm[cu] %t A210862 Flatten[%] (* A210862 *) %t A210862 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; %t A210862 TableForm[cv] %t A210862 Flatten[%] (* A210863 *) %Y A210862 Cf. A210863, A208510. %K A210862 nonn,tabl %O A210862 1,2 %A A210862 _Clark Kimberling_, Mar 28 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE