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 A271180 #17 Apr 02 2016 04:47:00
%S A271180 1,1,5,15,45,125,342,921,2461,6535,17282,45567,119898,315020,826830,
%T A271180 2168583,5684731,14896459,39024899,102216045,267693813,700997144,
%U A271180 1835543565,4806092673,12583591525,32946281848,86258240735,225834015840
%N A271180 Expansion of (4*x^3-7*x^2+4*x-1)/(x^6-4*x^5+4*x^4+x^3-7*x^2+5*x-1).
%H A271180 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,1,4,-4,1).
%F A271180 a(n) = (n+1)*Sum_{k=0..n} (Sum_{i=0..n-k} (binomial(i+k,i)*2^i*binomial(2*k+2,n-i-k)*(-1)^(n-i-k))/(k+1)*F(k+1)), where F = A000045 (Fibonacci numbers).
%F A271180 a(n) = 5*a(n-1) - 7*a(n-2) + a(n-3) + 4*a(n-4) - 4*a(n-5) + a(n-6) for n>3, a(0)=1, a(1)=1, a(2)=5, a(3)=15.
%t A271180 Table[(n + 1) Sum[Sum[(Binomial[i + k, i] 2^i Binomial[2 k + 2, n - i - k] (-1)^(n - i - k))/(k + 1) Fibonacci[k + 1], {i, 0, n - k}], {k, 0, n}], {n, 0, 27}] (* or *)
%t A271180 CoefficientList[Series[(4 x^3 - 7 x^2 + 4 x - 1)/(x^6 - 4 x^5 + 4 x^4 + x^3 - 7 x^2 + 5 x - 1), {x, 0, 27}], x] (* _Michael De Vlieger_, Apr 01 2016 *)
%o A271180 (Maxima) a(n):=(n+1)*sum(sum(binomial(i+k,i)*2^i*binomial(2*k+2,n-i-k)*(-1)^(n-i-k),i,0,n-k)/(k+1)*fib(k+1),k,0,n);
%o A271180 (PARI) x='x+O('x^99); Vec((4*x^3-7*x^2+4*x-1)/(x^6-4*x^5+4*x^4+x^3-7*x^2+5*x-1)) \\ _Altug Alkan_, Apr 01 2016
%Y A271180 Cf. A000045, A034008.
%K A271180 nonn,easy
%O A271180 0,3
%A A271180 _Vladimir Kruchinin_, Apr 01 2016