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%I #7 Jan 20 2014 03:41:54
%S 1,1,1,1,2,1,1,4,3,1,1,7,8,4,1,1,12,18,13,5,1,1,20,38,35,19,6,1,1,33,
%T 76,86,59,26,7,1,1,54,147,197,164,91,34,8,1,1,88,277,430,420,281,132,
%U 43,9,1,1,143,512,904,1014,792,447,183,53,10,1,1,232,932,1846,2338,2087,1371
%N Triangle read by rows, in which n-th row gives expansion of x^n/((1-x)(1-x-x^2)^n).
%C Riordan array (1/(1-x),x/(1-x-x^2)). - _Paul Barry_, Sep 13 2006
%F G.f.: (1-y-y^2) / [(1-y(1+y+z))(1-y)].
%F Number triangle T(n,k)=sum{j=0..n-k, sum{i=0..n-k-j, C(k+j-1,j)C(j,n-k-i-j)}}; - _Paul Barry_, Sep 13 2006
%F T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) - T(n-3,k), T(0,0) = T(1,0) = T(1,1) = T(2,0) = T(2,2) = 1, T(2,1) = 2, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Jan 20 2014
%e Rows begin {1},{1,1},{1,2,1},{1,4,3,1}...
%Y Row sums are A024537. Diagonal sums are A005578. Second column is A000071. Third column is A006478.
%Y Essentially the vertical partial sums of triangle A037027.
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Dec 25 2003
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