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 A233508 #13 Dec 16 2013 09:46:43
%S A233508 1,1,1,1,3,1,1,3,2,1,1,2,3,5,1,1,5,5,5,3,1,1,3,15,10,15,7,1,1,7,21,35,
%T A233508 35,21,4,1,1,4,14,28,35,28,14,9,1,1,9,18,42,63,63,42,18,5,1,1,5,45,60,
%U A233508 105,126,105,60,45,11,1
%N A233508 Numerators of the triangle of polynomial coefficients P(0,x)=1, 2*P(n)=(1+x)*((1+x)^(n-1)+x^(n-1)). Of the first array of A133135.
%C A233508 Discovered via Euler polynomials A060096(n)/A060097(n).
%C A233508 The fractional sequence is 1, 1, 1, 1/2, 3/2, 1, 1/2, 3/2, 2, 1, 1/2, 2, 3, 5/2, 1,... =a(n)/b(n). There is a correspondant sequence for Bernoulli polynomials (*).
%F A233508 a(n) = reduced A133138(n)/A007395.
%e A233508 1,
%e A233508 1, 1,
%e A233508 1, 3, 1,
%e A233508 1, 3, 2, 1,
%e A233508 1, 2, 3, 5, 1,
%e A233508 1, 5, 5, 5, 3, 1, etc.
%t A233508 p[n_] := (1+x)*((1+x)^(n-1)+x^(n-1))/2; t[n_, k_] := Coefficient[p[n], x, k] // Numerator; Table[t[n, k], {n, 0, 10 }, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Dec 16 2013 *)
%Y A233508 Cf. (*) A193815.
%K A233508 nonn,tabl,frac
%O A233508 0,5
%A A233508 _Paul Curtz_, Dec 11 2013