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 A026921 #26 Jun 01 2022 18:07:58
%S A026921 0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,2,1,1,0,0,2,1,2,1,1,0,1,2,3,2,2,1,
%T A026921 1,0,0,2,3,3,2,2,1,1,0,1,2,5,4,4,2,2,1,1,0,0,3,4,6,4,4,2,2,1,1,0,1,3,
%U A026921 7,7,7,5,4,2,2,1,1,0,0,3,6,10,8,7,5,4,2,2,1,1,0,1,3,9,11,13,9,8,5,4,2,2,1,1,0
%N A026921 Triangular array E by rows: E(n,k) = number of partitions of n into an even number of parts, the greatest being k.
%C A026921 The reversed rows (see example) stabilize to A027193. [_Joerg Arndt_, May 12 2013]
%F A026921 G.f. (including term a(0)=1): sum(n>=0, q^(2*n)/prod(k=1..2*n, 1-z*q^k) ), set z=1 to obtain g.f. for A027187. [_Joerg Arndt_, May 12 2013]
%F A026921 A026920(n,k) + E(n,k) = A008284(n,k). - _R. J. Mathar_, Aug 23 2019
%e A026921 G.f. = (1)*q^0 +
%e A026921 (0) * q^1 +
%e A026921 (1 + 0*z) * q^2 +
%e A026921 (0 + 1*z + 0*z^2) * q^3 +
%e A026921 (1 + 1*z + 1*z^2 + 0*z^3) * q^4 +
%e A026921 (0 + 1*z + 1*z^2 + 1*z^3 + 0*z^4) * q^5 +
%e A026921 (1 + 1*z + 2*z^2 + 1*z^3 + 1*z^4 + 0*z^5) * q^6 +
%e A026921 (0 + 2*z + 1*z^2 + 2*z^3 + 1*z^4 + 1*z^5 + 0*z^6) * q^7 +
%e A026921 ... [_Joerg Arndt_, May 12 2013]
%e A026921 Triangle starts:
%e A026921 01: [0]
%e A026921 02: [1, 0]
%e A026921 03: [0, 1, 0]
%e A026921 04: [1, 1, 1, 0]
%e A026921 05: [0, 1, 1, 1, 0]
%e A026921 06: [1, 1, 2, 1, 1, 0]
%e A026921 07: [0, 2, 1, 2, 1, 1, 0]
%e A026921 08: [1, 2, 3, 2, 2, 1, 1, 0]
%e A026921 09: [0, 2, 3, 3, 2, 2, 1, 1, 0]
%e A026921 10: [1, 2, 5, 4, 4, 2, 2, 1, 1, 0]
%e A026921 11: [0, 3, 4, 6, 4, 4, 2, 2, 1, 1, 0]
%e A026921 12: [1, 3, 7, 7, 7, 5, 4, 2, 2, 1, 1, 0]
%e A026921 13: [0, 3, 6, 10, 8, 7, 5, 4, 2, 2, 1, 1, 0]
%e A026921 14: [1, 3, 9, 11, 13, 9, 8, 5, 4, 2, 2, 1, 1, 0]
%e A026921 15: [0, 4, 8, 14, 14, 14, 9, 8, 5, 4, 2, 2, 1, 1, 0]
%e A026921 16: [1, 4, 12, 16, 20, 17, 15, 10, 8, 5, 4, 2, 2, 1, 1, 0]
%e A026921 17: [0, 4, 11, 20, 22, 23, 18, 15, 10, 8, 5, 4, 2, 2, 1, 1, 0]
%e A026921 18: [1, 4, 15, 23, 30, 28, 26, 19, 16, 10, 8, 5, 4, 2, 2, 1, 1, 0]
%e A026921 19: [0, 5, 13, 28, 33, 37, 31, 27, 19, 16, 10, 8, 5, 4, 2, 2, 1, 1, 0]
%e A026921 20: [1, 5, 18, 31, 44, 44, 43, 34, 28, 20, 16, 10, 8, 5, 4, 2, 2, 1, 1, 0]
%e A026921 ... [_Joerg Arndt_, May 12 2013]
%o A026921 (PARI)
%o A026921 N = 20; q = 'q + O('q^N);
%o A026921 gf = sum(n=0,N, q^(2*n)/prod(k=1, 2*n, 1-'z*q^k) );
%o A026921 v = Vec(gf);
%o A026921 { for(n=2, #v, /* print triangle starting with row 1: */
%o A026921 p = Pol('c0 +'cn*'z^n + v[n],'z);
%o A026921 p = polrecip(p);
%o A026921 p = Vec(p);
%o A026921 p[1] -= 'c0;
%o A026921 p = vector(#p-2, j, p[j]);
%o A026921 print(p);
%o A026921 ); }
%o A026921 /* _Joerg Arndt_, May 12 2013 */
%Y A026921 E(n, k) = O(n-k, 1)+O(n-k, 2)+...+O(n-k, m), where m=MIN{k, n-k}, n >= 2, O given by A026920.
%Y A026921 Columns k=3..6: A026927, A026928, A026929, A026930.
%K A026921 nonn,tabl
%O A026921 1,18
%A A026921 _Clark Kimberling_