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 A113607 #13 Mar 19 2025 23:35:14
%S A113607 1,2,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,11,11,1,1,1,1,26,66,26,1,1,1,1,57,
%T A113607 302,302,57,1,1,1,1,120,1191,2416,1191,120,1,1,1,1,247,4293,15619,
%U A113607 15619,4293,247,1,1,1,1,502,14608,88234,156190,88234,14608,502,1,1
%N A113607 An extended triangle of Eulerian coefficients A123125: f(x,n)=x^(n+1)+1+A123125(x,n).
%e A113607 Triangle starts:
%e A113607 1,
%e A113607 2, 1,
%e A113607 1, 1, 1,
%e A113607 1, 1, 1, 1,
%e A113607 1, 1, 4, 1, 1,
%e A113607 1, 1, 11, 11, 1, 1,
%e A113607 1, 1, 26, 66, 26, 1, 1,
%e A113607 1, 1, 57, 302, 302, 57, 1, 1,
%e A113607 1, 1, 120, 1191, 2416, 1191, 120, 1, 1,
%e A113607 1, 1, 247, 4293, 15619, 15619, 4293, 247, 1, 1,
%e A113607 1, 1, 502, 14608, 88234, 156190, 88234, 14608, 502, 1, 1,
%e A113607 ...
%t A113607 f[x_, n_] := f[x,n] = x^(n + 1) + (1 - x)^(n + 1)*Sum[k^n*x^k, {k, 0, Infinity}] + 1;
%t A113607 Table[FullSimplify[ExpandAll[f[x, n]]], {n, 0, 10}];
%t A113607 a = Join[{{1}}, Table[CoefficientList[FullSimplify[ExpandAll[f[x, n]]], x], {n, 0, 10}]];
%t A113607 Flatten[a]
%Y A113607 Cf. A123125.
%K A113607 nonn,tabl,less
%O A113607 1,2
%A A113607 _Roger L. Bagula_ and _Gary W. Adamson_, Aug 25 2008