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 A307040 #18 May 26 2021 00:55:45
%S A307040 1,1,1,1,1,1,0,-6,-27,-83,-209,-461,-922,-1702,-2911,-4549,-6187,
%T A307040 -6187,0,23238,87021,238337,564719,1217483,2434966,4542526,7865521,
%U A307040 12403951,16942381,16942381,0,-63239286,-236031147,-644886923,-1525870529,-3287837741,-6575675482
%N A307040 a(n) = Sum_{k=0..floor(n/6)} (-1)^k*binomial(n,6*k).
%H A307040 Seiichi Manyama, <a href="/A307040/b307040.txt">Table of n, a(n) for n = 0..3000</a>
%H A307040 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-2).
%F A307040 G.f.: (1 - x)^5/((1 - x)^6 + x^6).
%F A307040 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - 2*a(n-6) for n > 5.
%t A307040 a[n_] := Sum[(-1)^k * Binomial[n,6*k], {k,0,Floor[n/6]}]; Array[a, 37, 0] (* _Amiram Eldar_, May 25 2021 *)
%o A307040 (PARI) {a(n) = sum(k=0, n\6, (-1)^k*binomial(n, 6*k))}
%o A307040 (PARI) N=66; x='x+O('x^N); Vec((1-x)^5/((1-x)^6+x^6))
%Y A307040 Column 6 of A307039.
%Y A307040 Cf. A306847.
%K A307040 sign,easy
%O A307040 0,8
%A A307040 _Seiichi Manyama_, Mar 21 2019