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 A242618 #29 Dec 12 2016 02:28:24
%S A242618 1,1,1,0,1,1,2,2,1,1,1,4,2,1,1,2,3,3,2,1,8,3,3,2,4,6,5,5,4,13,8,4,1,5,
%T A242618 5,11,13,7,1,11,20,14,9,2,1,6,13,17,26,11,3,1,22,31,27,15,5,2,12,18,
%U A242618 34,44,18,7,4,40,47,51,23,11,5,16,36,56,72,34,11,1
%N A242618 Number T(n,k) of partitions of n, where k is the difference between the number of odd parts and the number of even parts, both counted without multiplicity; triangle T(n,k), n>=0, read by rows.
%C A242618 T(n,0) = A241638(n).
%C A242618 Sum_{k<0} T(n,k) = A241640(n).
%C A242618 Sum_{k<=0} T(n,k) = A241639(n).
%C A242618 Sum_{k>=0} T(n,k) = A241637(n).
%C A242618 Sum_{k>0} T(n,k) = A241636(n).
%C A242618 T(n^2,n) = T(n^2+n,-n) = 1.
%C A242618 T(n^2+n,n) = Sum_{k} T(n,k) = A000041(n).
%C A242618 T(n^2+3*n,-n) = A000712(n).
%H A242618 Alois P. Heinz, <a href="/A242618/b242618.txt">Rows n = 0..500, flattened</a>
%e A242618 Triangle T(n,k) begins:
%e A242618 : n\k : -3 -2 -1 0 1 2 3 ...
%e A242618 +-----+---------------------------
%e A242618 : 0 : 1;
%e A242618 : 1 : 1;
%e A242618 : 2 : 1, 0, 1;
%e A242618 : 3 : 1, 2;
%e A242618 : 4 : 2, 1, 1, 1;
%e A242618 : 5 : 4, 2, 1;
%e A242618 : 6 : 1, 2, 3, 3, 2;
%e A242618 : 7 : 1, 8, 3, 3;
%e A242618 : 8 : 2, 4, 6, 5, 5;
%e A242618 : 9 : 4, 13, 8, 4, 1;
%e A242618 : 10 : 5, 5, 11, 13, 7, 1;
%e A242618 : 11 : 11, 20, 14, 9, 2;
%e A242618 : 12 : 1, 6, 13, 17, 26, 11, 3;
%e A242618 : 13 : 1, 22, 31, 27, 15, 5;
%e A242618 : 14 : 2, 12, 18, 34, 44, 18, 7;
%p A242618 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A242618 expand(b(n, i-1)+add(b(n-i*j, i-1)*x^(2*irem(i, 2)-1), j=1..n/i))))
%p A242618 end:
%p A242618 T:= n-> (p-> seq(coeff(p, x, i), i=ldegree(p)..degree(p)))(b(n$2)):
%p A242618 seq(T(n), n=0..20);
%t A242618 b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Expand[b[n, i - 1] + Sum[b[n - i*j, i - 1]*x^(2*Mod[i, 2] - 1), {j, 1, n/i}]]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, Exponent[p, x, Min], Exponent[p, x]}]][b[n, n]]; Table[T[n], {n, 0, 20}] // Flatten (* _Jean-François Alcover_, Dec 12 2016 after _Alois P. Heinz_ *)
%Y A242618 Columns k=(-10)-10 give: A242682, A242683, A242684, A242685, A242686, A242687, A242688, A242689, A242690, A242691, A241638, A242692, A242693, A242694, A242695, A242696, A242697, A242698, A242699, A242700, A242701.
%Y A242618 Row sums give A000041.
%Y A242618 Cf. A240009 (parts counted with multiplicity), A240021 (distinct parts), A242626 (compositions counted without multiplicity).
%K A242618 nonn,tabf,look
%O A242618 0,7
%A A242618 _Alois P. Heinz_, May 19 2014