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 A317509 #17 Aug 08 2025 23:29:19
%S A317509 1,-1,1,-1,1,1,-3,5,-7,9,-7,1,9,-23,41,-55,57,-39,-7,89,-199,313,-391,
%T A317509 377,-199,-199,825,-1607,2361,-2759,2361,-711,-2503,7225,-12743,17465,
%U A317509 -18887,13881,569,-26055,60985,-98759,126521
%N A317509 Coefficients in expansion of 1/(1 + x - 2*x^5).
%C A317509 Coefficients in expansion of 1/(1 + x - 2*x^5) are given by the sum of numbers along "fourth Layer" skew diagonals pointing top-left in triangle A065109 ((2-x)^n) and by the sum of numbers along "fourth Layer" skew diagonals pointing top-right in triangle A303872 ((-1+2*x)^n), see links.
%D A317509 Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3.
%H A317509 Shara Lalo, <a href="/A317509/a317509.pdf">Fourth layer skew diagonals in center-justified triangle of coefficients in expansion of (2 - x)^n</a>
%H A317509 Shara Lalo, <a href="/A317509/a317509_1.pdf">Fourth layer skew diagonals in center-justified triangle of coefficients in expansion of (-1 + 2x)^n</a>
%H A317509 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,0,0,2).
%F A317509 a(0)=1, a(n) = -1 * a(n-1) + 2 * a(n-5) for n >= 0; a(n)=0 for n < 0.
%t A317509 CoefficientList[Series[1/(1 + x - 2 x^5), {x, 0, 42}], x]
%t A317509 a[0] = 1; a[n_] := a[n] = If[n < 0, 0, - a[n - 1] + 2 * a[n - 5]]; Table[a[n], {n, 0, 42}] // Flatten
%t A317509 LinearRecurrence[{-1,0,0,0,2}, {1,-1,1,-1,1}, 43]
%o A317509 (PARI) my(x='x+O('x^99)); Vec(1/(1+x-2*x^5)) \\ _Altug Alkan_, Sep 04 2018
%Y A317509 Cf. A065109, A303872.
%K A317509 sign,easy
%O A317509 0,7
%A A317509 _Shara Lalo_, Sep 04 2018