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 A306940 #18 May 31 2021 13:11:21
%S A306940 1,6,21,56,126,252,461,780,1209,1638,1638,0,-6187,-23238,-63783,
%T A306940 -151316,-326382,-652764,-1217483,-2107560,-3322995,-4538430,-4538430,
%U A306940 0,16942381,63239286,172791861,408855776,880983606,1761967212,3287837741,5694626340
%N A306940 Expansion of 1/((1 - x)^6 + x^6).
%H A306940 Seiichi Manyama, <a href="/A306940/b306940.txt">Table of n, a(n) for n = 0..3000</a>
%H A306940 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-2).
%F A306940 a(n) = Sum_{k=0..floor(n/6)} (-1)^k*binomial(n+5,6*k+5).
%F A306940 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 A306940 CoefficientList[Series[1/((1 - x)^6 + x^6), {x, 0, 31}], x] (* _Amiram Eldar_, May 25 2021 *)
%t A306940 LinearRecurrence[{6,-15,20,-15,6,-2},{1,6,21,56,126,252},40] (* _Harvey P. Dale_, May 31 2021 *)
%o A306940 (PARI) {a(n) = sum(k=0, n\6, (-1)^k*binomial(n+5, 6*k+5))}
%o A306940 (PARI) N=66; x='x+O('x^N); Vec(1/((1-x)^6+x^6))
%Y A306940 Column 6 of A306914.
%K A306940 sign,easy
%O A306940 0,2
%A A306940 _Seiichi Manyama_, Mar 17 2019