%I #16 Mar 30 2012 17:34:05
%S 1,1,2,1,2,3,1,2,3,1,5,1,2,3,1,5,1,7,1,2,3,1,5,1,7,1,2,1,11,1,2,3,1,5,
%T 1,7,1,2,1,11,1,2,1,15,1,2,3,1,5,1,7,1,2,1,11,1,2,1,15,1,2,1,4,1,1,22,
%U 1,2,3,1,5,1,7,1,2,1,11,1,2,1,15
%N Triangle read by rows: T(n,k) = number of parts in the k-th region of n.
%e Triangle begins:
%e 1;
%e 1,2;
%e 1,2,3;
%e 1,2,3,1,5;
%e 1,2,3,1,5,1,7;
%e 1,2,3,1,5,1,7,1,2,1,11;
%e 1,2,3,1,5,1,7,1,2,1,11,1,2,1,15;
%e 1,2,3,1,5,1,7,1,2,1,11,1,2,1,15,1,2,1,4,1,1,22;
%e ...
%e Row n has length A000041(n). Row sums give A006128, n >= 1. Right border gives A000041, n >= 1. Records in every row give A000041, n >= 1. Rows converge to A194446.
%Y Cf. A000041, A006128, A135010, A138121, A186114, A186412, A193870, A194437, A194438, A194439, A194446, A194447.
%K nonn,tabf
%O 1,3
%A _Omar E. Pol_, Nov 27 2011