This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177717 #4 Jun 02 2025 02:55:52
%S A177717 2,1,1,2,0,2,1,2,2,1,2,0,6,0,2,1,3,4,4,3,1,2,0,11,0,11,0,2,1,4,6,10,
%T A177717 10,6,4,1,2,0,17,0,30,0,17,0,2,1,5,8,20,21,21,20,8,5,1
%N A177717 A symmetrical triangle based on the Fibonacci Polynomials: p(x,n)=f(n,x)+x^(n-1)*f(n,1/x).
%C A177717 Row sums are:
%C A177717 {2, 2, 4, 6, 10, 16, 26, 42, 68, 110,...}
%D A177717 Function form used from:http://functions.wolfram.com/HypergeometricFunctions/Fibonacci2General/26/01/02/0001/
%F A177717 f(x,n)=(1/(2 Sqrt[4 + z^2])) (-HypergeometricPFQ[{}, {}, n ((-I) Pi - Log[(1/2) (z + \ Sqrt[4 + z^2])])] - HypergeometricPFQ[{}, {}, n (I Pi - Log[(1/2) (z + Sqrt[ 4 + z^2])])] + 2 HypergeometricPFQ[{}, {}, n Log[(1/2) (z + Sqrt[4 + z^2])]]);
%F A177717 p(x,n)=f(x,n)+x^(n-1)*f(1/x,n);
%F A177717 t(n,m)=coefficients(p(x,n))
%e A177717 {2},
%e A177717 {1, 1},
%e A177717 {2, 0, 2},
%e A177717 {1, 2, 2, 1},
%e A177717 {2, 0, 6, 0, 2},
%e A177717 {1, 3, 4, 4, 3, 1},
%e A177717 {2, 0, 11, 0, 11, 0, 2},
%e A177717 {1, 4, 6, 10, 10, 6, 4, 1},
%e A177717 {2, 0, 17, 0, 30, 0, 17, 0, 2},
%e A177717 {1, 5, 8, 20, 21, 21, 20, 8, 5, 1}
%t A177717 f[n_, z_] := (1/(2 Sqrt[4 + z^2])) (-HypergeometricPFQ[{}, {}, n ((-I) Pi - \ Log[(1/2) (z + Sqrt[4 + z^2])])] - HypergeometricPFQ[{}, {}, n (I Pi - Log[( 1/2) (z + Sqrt[4 + z^2])])] + 2 HypergeometricPFQ[{}, {}, n Log[(1/ 2) (z + Sqrt[4 + z^2])]]);
%t A177717 Table[CoefficientList[FullSimplify[ExpandAll[f[n, x] + x^(n - 1)*f[n, 1/x]]], x], {n, 1, 10}];
%t A177717 Flatten[%]
%Y A177717 Cf. A168561
%K A177717 nonn,tabl,uned
%O A177717 0,1
%A A177717 _Roger L. Bagula_, May 12 2010