%I A108041
%S A108041 1,1,2,2,3,7,7,9,19,42,42,49,100,210,443,443,485,977,2005,4120,8473,8473,
%T A108041 8916,17874,36240,73508,149131,302615,302615,311088,622619,1254196,2526758,
%U A108041 5090784,10257191,20667866,20667866,20970481,41949435,84210401,169052379
%N A108041 Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n,
               0)=a(n-1,n-1), a(n,k)=a(n,k-1) + Sum_{i=0..k-1} a(n-1,i).
%e A108041 1; 1,2; 2,3,7; 7,9,19,42; 42,49,100,210,443; ...
%p A108041 f := proc(n,k) local i,t1; option remember; if n=0 and k=0 then 1 elif 
               k=0 then f(n-1,n-1) else add(f(n,i),i=0..k-1) +f(n-1,k-1); fi: end;
%Y A108041 Borders give A108042. Row sums are A108043. Cf. A011971.
%Y A108041 Sequence in context: A002583 A068519 A083702 this_sequence A095017 A141559 
               A160433
%Y A108041 Adjacent sequences: A108038 A108039 A108040 this_sequence A108042 A108043 
               A108044
%K A108041 tabl,nonn
%O A108041 0,3
%A A108041 N. J. A. Sloane (njas(AT)research.att.com), Jun 01 2005