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 A099253 #16 Oct 12 2022 09:34:36
%S A099253 1,8,43,211,1030,5055,24851,122166,600470,2951330,14505951,71297834,
%T A099253 350434385,1722411860,8465785506,41609980404,204516223418,
%U A099253 1005212819668,4940697593195,24283905085013,119357243593561,586649945651116
%N A099253 (7*n+6)-th terms of expansion of 1/(1-x-x^7).
%H A099253 G. C. Greubel, <a href="/A099253/b099253.txt">Table of n, a(n) for n = 0..500</a>
%H A099253 D. Birmajer, J. B. Gil, and M. D. Weiner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Gil/gil6.html">On the Enumeration of Restricted Words over a Finite Alphabet</a>, J. Int. Seq. 19 (2016) # 16.1.3, example 16.
%H A099253 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-21,35,-35,21,-7,1).
%F A099253 G.f.: 1/((1-x)^7 - x);
%F A099253 Equals A099239(n, 7).
%F A099253 a(n) = 8*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7).
%F A099253 a(n) = Sum_{k=0..n} binomial(7*n - 6*(k-1), k).
%F A099253 a(n) = Sum_{k=0..n} binomial(n + 6*(k+1), k + 6*(k+1)).
%F A099253 a(n) = Sum_{k=0..n} binomial(n + 6*(k+1), n-k).
%t A099253 Table[Sum[Binomial[7*n-6*(j-1), j], {j,0,n}], {n,0,30}] (* _G. C. Greubel_, Mar 09 2021 *)
%o A099253 (Sage) [sum(binomial(7*n-6*j+6,j) for j in (0..n)) for n in (0..30)] # _G. C. Greubel_, Mar 09 2021
%o A099253 (Magma) [(&+[Binomial(7*n-6*j+6,j): j in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Mar 09 2021
%Y A099253 Cf. A099239.
%K A099253 easy,nonn
%O A099253 0,2
%A A099253 _Paul Barry_, Oct 08 2004