# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a156135 Showing 1-1 of 1 %I A156135 #4 Jul 25 2019 01:12:12 %S A156135 1,0,-1,1,0,1,-2,1,0,1,-3,1,1,0,1,-4,-4,1,0,-1,8,9,-23,6,1,0,1,-13, %T A156135 -41,106,-41,-13,1,0,1,-21,-146,484,-152,-186,19,1,0,1,-33,-492,1784, %U A156135 1784,-492,-33,1,0,-1,55,1359,-10701,-8552,27128,-7875,-1467,53,1,0,1,-89 %N A156135 Denominator coefficients of infinite over the Fibonacci sequence: p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Numerator(p(x,n)). %C A156135 Row sums are: %C A156135 {1, 0, 0, 0, -6, 0, 0, 0, 2520, 0, 0,...}. %C A156135 The denominator and numerator polynomials appear to be new. %F A156135 p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Numerator(p(x,n)). %e A156135 {1}, %e A156135 {0, -1, 1}, %e A156135 {0, 1, -2, 1}, %e A156135 {0, 1, -3, 1, 1}, %e A156135 {0, 1, -4, -4, 1}, %e A156135 {0, -1, 8, 9, -23, 6, 1}, %e A156135 {0, 1, -13, -41, 106, -41, -13, 1}, %e A156135 {0, 1, -21, -146, 484, -152, -186, 19, 1}, %e A156135 {0, 1, -33, -492, 1784, 1784, -492, -33, 1}, %e A156135 {0, -1, 55, 1359, -10701, -8552, 27128, -7875, -1467, 53, 1}, %e A156135 {0, 1, -89, -3872, 50193, 117271, -327008, 117271, 50193, -3872, -89, 1} %t A156135 Clear[t0, p, x, n, m]; %t A156135 p[x_, n_] = (1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}] %t A156135 Table[Numerator[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}]; %t A156135 Table[CoefficientList[Numerator[FullSimplify[ExpandAll[p[x, n]]]], x], {n, 0, 10}]; %t A156135 Flatten[%] %Y A156135 A000045 %K A156135 sign,tabl,uned %O A156135 0,7 %A A156135 _Roger L. Bagula_, Feb 04 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE