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 A171414 #9 Jan 13 2019 12:07:31
%S A171414 1,1,1,1,1,1,1,2,3,3,2,1,1,2,3,4,5,4,3,2,1,1,3,6,10,15,19,21,21,19,15,
%T A171414 10,6,3,1,1,3,6,10,15,21,28,33,36,37,36,33,28,21,15,10,6,3,1,1,4,10,
%U A171414 20,35,56,84,117,152,186,216,239,252,252,239,216,186,152,117,84,56,35,20,10,4,1
%N A171414 Triangle read by rows (n >= 1): T(n,k) = [x^k] p(x,n), where p(x,n) = ((x^n - 1)/(x - 1))^floor(n/2) if n is odd, and p(x,n) = ((x^n - 1)/(x - 1))*p(x,n-1) otherwise.
%e A171414 Triangle begins:
%e A171414 1;
%e A171414 1, 1;
%e A171414 1, 1, 1;
%e A171414 1, 2, 3, 3, 2, 1;
%e A171414 1, 2, 3, 4, 5, 4, 3, 2, 1;
%e A171414 1, 3, 6, 10, 15, 19, 21, 21, 19, 15, 10, 6, 3, 1;
%e A171414 1, 3, 6, 10, 15, 21, 28, 33, 36, 37, 36, 33, 28, 21, 15, 10, 6, 3, 1;
%e A171414 ...
%t A171414 p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, Sum[x^i, {i, 0, n - 1}]*p[x, n - 1], (Sum[x^i, {i, 0, n - 1}])^Floor[n/2]]
%t A171414 Flatten[Table[CoefficientList[p[x, n], x], {n, 1, 12}]]
%o A171414 (Maxima)
%o A171414 p(x, n) := if mod(n, 2) = 0 then ((x^n - 1)/(x - 1))*p(x, n - 1) else ((x^n - 1)/(x - 1))^floor(n/2)$
%o A171414 T(n, k) := ratcoef(p(x, n), x, k)$
%o A171414 create_list(T(n, k), n, 1, 10, k, 0, hipow(fullratsimp(p(x, n)), x));
%o A171414 /* _Franck Maminirina Ramaharo_, Jan 13 2019 */
%Y A171414 Cf. A008406, A171412.
%K A171414 nonn,easy,tabf
%O A171414 1,8
%A A171414 _Roger L. Bagula_, Dec 08 2009
%E A171414 Edited by _Franck Maminirina Ramaharo_, Jan 13 2019