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 A194438 #28 May 24 2021 00:19:37 %S A194438 1,1,1,1,1,1,2,1,1,0,1,3,1,1,0,1,0,1,5,2,1,0,1,0,1,0,0,0,1,7,3,1,0,1, %T A194438 0,1,0,0,0,1,0,0,0,1,11,4,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,15, %U A194438 6,1,2,1,0,1,0,0,0,1,0,0,0,1,0,0 %N A194438 Triangle read by rows: T(n,k) is the number of regions of the set of partitions of n into k parts. %C A194438 For the definition of "region" see A206437. See also A186114 and A193870. - _Omar E. Pol_, May 21 2021 %H A194438 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a> %e A194438 Triangle begins: %e A194438 1; %e A194438 1,1; %e A194438 1,1,1; %e A194438 2,1,1,0,1; %e A194438 3,1,1,0,1,0,1; %e A194438 5,2,1,0,1,0,1,0,0,0,1; %e A194438 7,3,1,0,1,0,1,0,0,0,1,0,0,0,1; %e A194438 11,4,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1; %e A194438 ... %Y A194438 Column 1 is A194439. %Y A194438 Row n has length A000041(n). %Y A194438 Row sums give A000041, n >= 1. %Y A194438 Cf. A008284, A135010, A138121, A186114, A186412, A193870, A194436, A194437, A194439, A194446, A194447, A206437. %K A194438 nonn,tabf %O A194438 1,7 %A A194438 _Omar E. Pol_, Nov 28 2011 %E A194438 Definition clarified by _Omar E. Pol_, May 21 2021