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 A049018 #26 Sep 08 2022 08:44:58
%S A049018 1,-7,28,-84,210,-462,924,-1715,2989,-4900,7448,-9996,9996,0,-38759,
%T A049018 149205,-422576,1041348,-2350922,4970070,-9940140,18874261,-33957343,
%U A049018 57374296,-89125120,120875944,-120875944,0,459957169,-1749692735,4904887652
%N A049018 Expansion of 1/((1+x)^7 - x^7).
%C A049018 It appears that the (unsigned) sequence is identical to its 7th-order absolute difference. - _John W. Layman_, Oct 02 2003
%H A049018 Seiichi Manyama, <a href="/A049018/b049018.txt">Table of n, a(n) for n = 0..3000</a>
%H A049018 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-7, -21, -35, -35, -21, -7).
%F A049018 a(n) = (-1)^n * Sum_{k=0..floor(n/7)} (-1)^k * binomial(n+6,7*k+6). - _Seiichi Manyama_, Mar 21 2019
%t A049018 LinearRecurrence[{-7,-21,-35,-35,-21,-7},{1,-7,28,-84,210,-462}, 35] (* _Ray Chandler_, Sep 23 2015 *)
%o A049018 (PARI) Vec(1/((1+x)^7-x^7)+O(x^35)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o A049018 (PARI) {a(n) = (-1)^n*sum(k=0, n\7, (-1)^k*binomial(n+6, 7*k+6))} \\ _Seiichi Manyama_, Mar 21 2019
%o A049018 (Magma) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( 1/((1+x)^7 - x^7) )); // _G. C. Greubel_, Mar 17 2019
%o A049018 (Sage) (1/((1+x)^7 - x^7)).series(x, 35).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 17 2019
%Y A049018 Column 7 of A307047.
%Y A049018 Cf. A049017.
%K A049018 sign,easy
%O A049018 0,2
%A A049018 _N. J. A. Sloane_