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 A098173 #14 Sep 08 2022 08:45:14 %S A098173 1,0,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,0,5,1,0,0,0,0,0,15,1,0,0,0,0,0,0, %T A098173 35,1,0,0,0,0,0,0,1,70,1,0,0,0,0,0,0,0,9,126,1,0,0,0,0,0,0,0,0,45,210, %U A098173 1,0,0,0,0,0,0,0,0,0,165,330,1,0,0,0,0,0,0,0,0,0,1,495,495,1 %N A098173 Triangle T(n,k) with diagonals T(n,n-k) = binomial(n, 4k). %C A098173 Row sums are A038503. %H A098173 Seiichi Manyama, <a href="/A098173/b098173.txt">Rows n = 0..139, flattened</a> %F A098173 Triangle T(n, k) = binomial(n, 4(n-k)). %e A098173 Rows begin %e A098173 {1}, %e A098173 {0,1}, %e A098173 {0,0,1}, %e A098173 {0,0,0,1}, %e A098173 {0,0,0,1,1}, %e A098173 {0,0,0,0,5,1}, %e A098173 ... %t A098173 Table[Binomial[n, 4(n-k)], {n, 0, 12}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Mar 15 2019 *) %o A098173 (PARI) {T(n, k) = binomial(n, 4*(n-k))}; \\ _G. C. Greubel_, Mar 15 2019 %o A098173 (Magma) [[Binomial(n, 4*(n-k)): k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, Mar 15 2019 %o A098173 (Sage) [[binomial(n, 4*(n-k)) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Mar 15 2019 %o A098173 (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, 4*(n-k)) ))); # _G. C. Greubel_, Mar 15 2019 %Y A098173 Cf. A098158, A098172. %K A098173 easy,nonn,tabl %O A098173 0,20 %A A098173 _Paul Barry_, Aug 30 2004