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 A307041 #17 May 26 2021 00:55:54
%S A307041 1,1,1,1,1,1,1,0,-7,-35,-119,-329,-791,-1715,-3430,-6419,-11319,
%T A307041 -18767,-28763,-38759,-38759,0,149205,571781,1613129,3964051,8934121,
%U A307041 18874261,37748522,71705865,129080161,218205281,339081225,459957169,459957169,0,-1749692735
%N A307041 a(n) = Sum_{k=0..floor(n/7)} (-1)^k*binomial(n,7*k).
%H A307041 Seiichi Manyama, <a href="/A307041/b307041.txt">Table of n, a(n) for n = 0..3000</a>
%H A307041 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7).
%F A307041 G.f.: (1 - x)^6/((1 - x)^7 + x^7).
%F A307041 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) for n > 6.
%t A307041 a[n_] := Sum[(-1)^k * Binomial[n,7*k], {k,0,Floor[n/7]}]; Array[a, 37, 0] (* _Amiram Eldar_, May 25 2021 *)
%o A307041 (PARI) {a(n) = sum(k=0, n\7, (-1)^k*binomial(n, 7*k))}
%o A307041 (PARI) N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7+x^7))
%Y A307041 Column 7 of A307039.
%Y A307041 Cf. A306852.
%K A307041 sign,easy
%O A307041 0,9
%A A307041 _Seiichi Manyama_, Mar 21 2019