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%I #3 Mar 30 2012 16:50:16
%S 1,1,2,2,3,7,7,9,19,42,42,49,100,210,443,443,485,977,2005,4120,8473,
%T 8473,8916,17874,36240,73508,149131,302615,302615,311088,622619,
%U 1254196,2526758,5090784,10257191,20667866,20667866,20970481,41949435,84210401,169052379
%N 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 1; 1,2; 2,3,7; 7,9,19,42; 42,49,100,210,443; ...
%p 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 Borders give A108042. Row sums are A108043. Cf. A011971.
%K tabl,nonn
%O 0,3
%A _N. J. A. Sloane_, Jun 01 2005
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