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 A046223 #15 Jul 02 2025 16:01:56
%S A046223 1,1,2,1,1,3,1,11,1,40,1,147,1,546,1,2046,1,7722,1,29315,1,111826,1,
%T A046223 428298,1,1646008,1,6344366,1,24515700,1,94942620,1,368404110,1,
%U A046223 1431985635,1,5574725970,1,21732560850,1,84828633120,1,331488081210,1
%N A046223 First denominator and then numerator of central elements of 1/2-Pascal triangle.
%C A046223 a(n) = A046222(n-1) for n > 5. - _Georg Fischer_, Oct 17 2018
%H A046223 Michael De Vlieger, <a href="/A046223/b046223.txt">Table of n, a(n) for n = 1..3000</a>
%e A046223 1/1; 1/1 1/1; 1/1 1/2 1/1; 1/1 3/2 3/2 1/1; 1/1 5/2 3/1 5/2 1/1; 1/1 7/2 11/2 11/2 7/2 1/1; 1/1 9/2 9/1 11/1 9/1 9/2 1/1; 1/1 11/2 27/2 20/1 20/1 27/2 11/2 1/1; ...
%t A046223 Map[{Denominator@ #, Numerator@ #} &@ #[[Ceiling[Length[#]/2] ]] &, Select[Nest[Append[#, Join[{#[[-1, 1]]}, Total /@ Partition[#[[-1]], 2, 1], {#[[-1, -1]]}]] &, {{1}, {1, 1}, {1, 1/2, 1}}, 2 (20) + 1], OddQ@ Length@ # & ]] // Flatten (* or *)
%t A046223 With[{r = Sqrt[1 - 4 x]}, {1, 1, 2, 1}~Join~Riffle[ConstantArray[1, Length@ #], #] &@ CoefficientList[Series[(2 - 2 r - 3 x - r x)/(2 r x^2), {x, 0, 19}], x]] (* _Michael De Vlieger_, Oct 17 2018 *)
%Y A046223 Cf. A046213, A046222.
%K A046223 nonn
%O A046223 1,3
%A A046223 _Mohammad K. Azarian_
%E A046223 More terms from _James Sellers_, Dec 13 1999