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 A242498 #23 Feb 11 2015 11:14:19
%S A242498 1,1,1,0,0,1,2,1,0,1,1,1,0,3,2,0,1,3,4,1,4,3,0,1,1,2,1,6,9,3,5,4,0,1,
%T A242498 4,9,6,11,16,6,6,5,0,1,1,3,3,11,24,18,19,25,10,7,6,0,1,5,16,18,28,51,
%U A242498 40,31,36,15,8,7,0,1,1,4,6,19,51,60,65,95,75,48,49,21,9,8,0,1
%N A242498 Number T(n,k) of compositions of n, where k is the difference between the number of odd parts and the number of even parts; triangle T(n,k), n>=0, -floor(n/2)+(n mod 2)<=k<=n, read by rows.
%C A242498 T(n,k) = T(n+k,-k).
%H A242498 Alois P. Heinz, <a href="/A242498/b242498.txt">Rows n = 0..120, flattened</a>
%e A242498 Triangle T(n,k) begins:
%e A242498 : n\k : -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ...
%e A242498 +-----+---------------------------------------------------------
%e A242498 : 0 : 1;
%e A242498 : 1 : 1;
%e A242498 : 2 : 1, 0, 0, 1;
%e A242498 : 3 : 2, 1, 0, 1;
%e A242498 : 4 : 1, 1, 0, 3, 2, 0, 1;
%e A242498 : 5 : 3, 4, 1, 4, 3, 0, 1;
%e A242498 : 6 : 1, 2, 1, 6, 9, 3, 5, 4, 0, 1;
%e A242498 : 7 : 4, 9, 6, 11, 16, 6, 6, 5, 0, 1;
%e A242498 : 8 : 1, 3, 3, 11, 24, 18, 19, 25, 10, 7, 6, 0, 1;
%e A242498 : 9 : 5, 16, 18, 28, 51, 40, 31, 36, 15, 8, 7, 0, 1;
%e A242498 : 10 : 1, 4, 6, 19, 51, 60, 65, 95, 75, 48, 49, 21, 9, 8, 0, 1;
%p A242498 b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0, expand(
%p A242498 add(x^(j*(2*irem(i, 2)-1))*b(n-i*j, i-1, p+j)/j!, j=0..n/i))))
%p A242498 end:
%p A242498 T:= n-> (p-> seq(coeff(p, x, i), i=ldegree(p)..degree(p)))(b(n$2, 0)):
%p A242498 seq(T(n), n=0..20);
%t A242498 b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i<1, 0, Expand[Sum[x^(j*(2*Mod[i, 2]-1))*b[n-i*j, i-1, p+j]/j!, {j, 0, n/i}]]]] ; T[n_] := Function[{p}, Table[ Coefficient[p, x, i], {i, Exponent[p, x, Min], Exponent[p, x]}]][b[n, n, 0]]; Table[T[n], {n, 0, 20}] // Flatten (* _Jean-François Alcover_, Feb 11 2015, after _Alois P. Heinz_ *)
%Y A242498 Columns k=0-10 gives: A098123, A242499, A242500, A242501, A242502, A242503, A242504, A242505, A242506, A242507, A242508.
%Y A242498 Row sums give A011782.
%Y A242498 Diagonals include: A000012, A000004, A001477, A000217, A000290, A180415.
%Y A242498 Row lengths give A016777(floor(n/2)).
%Y A242498 Cf. A240009, A240021.
%K A242498 nonn,tabf
%O A242498 0,7
%A A242498 _Alois P. Heinz_, May 16 2014