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 A382232 #22 Apr 25 2025 20:40:30
%S A382232 1,1,1,1,1,3,3,1,1,9,26,26,9,1,1,23,165,387,387,165,23,1,1,53,860,
%T A382232 4292,9194,9194,4292,860,53,1,1,115,3967,38885,160778,314654,314654,
%U A382232 160778,38885,3967,115,1,1,241,17022,307454,2291375,8041695,14743812,14743812,8041695,2291375,307454,17022,241,1
%N A382232 Irregular triangle read by rows: T(n,k) = [x^k] (1+x) * A_n(x)^2, where A_n(x) is the n-th Eulerian polynomial.
%H A382232 Ryuichi Sakamoto, <a href="https://arxiv.org/abs/1904.10667">The h*-polynomial of the cut polytope of K_{2,m} in the lattice spanned by its vertices</a>, arXiv:1904.10667 [math.CO], 2019.
%H A382232 Ryuichi Sakamoto, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Sakamoto/saka6.html">The h*-polynomial of the cut polytope of K_{2,m} in the lattice spanned by its vertices</a>, Journal of Integer Sequences, Vol. 23, 2020, #20.7.5.
%H A382232 OEIS Wiki, <a href="http://oeis.org/wiki/Eulerian_polynomials">Eulerian polynomials</a>.
%F A382232 T(n,k) = T(n,2*n-1-k) for n > 0.
%e A382232 Irregular triangle begins:
%e A382232 1, 1;
%e A382232 1, 1;
%e A382232 1, 3, 3, 1;
%e A382232 1, 9, 26, 26, 9, 1;
%e A382232 1, 23, 165, 387, 387, 165, 23, 1;
%e A382232 1, 53, 860, 4292, 9194, 9194, 4292, 860, 53, 1;
%e A382232 ...
%o A382232 (PARI) a(n) = sum(k=0, n, k!*stirling(n, k, 2)*(x-1)^(n-k));
%o A382232 T(n, k) = polcoef((1+x)*a(n)^2, k);
%o A382232 for(n=0, 7, for(k=0, 2*(n+0^n)-1, print1(T(n, k), ", ")));
%Y A382232 Row sums give A048617.
%Y A382232 Cf. A125300, A165889, A173018.
%K A382232 nonn,tabf
%O A382232 0,6
%A A382232 _Seiichi Manyama_, Mar 19 2025