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%I #8 Mar 31 2012 10:23:12
%S 1,1,1,2,2,1,4,5,3,1,8,12,9,4,1,17,28,25,14,5,1,33,66,66,44,20,6,1,66,
%T 148,171,129,70,27,7,1,132,330,425,364,225,104,35,8,1,264,728,1035,
%U 984,686,363,147,44,9,1,529,1592,2475,2584,1995,1188,553,200,54,10,1,1057,3459,5830,6624,5600,3689,1932,806,264,65,11,1
%N Triangle T(n,m) = coefficient of x^n in expansion of [x/(1-x-x^2-x^3-x^4-2*x^5)]^m = sum(n>=m, T(n,m) x^n).
%F T(n,i):=sum(k=0..n-i, binomial(k+i-1,i-1)*sum(r=0..k, binomial(k,r)*sum(m=0..r, binomial(r,m)*sum(j=0..m, binomial(j,-r+n-m-k-j-i)*binomial(m,j)*2^(-r+n-m-k-j-i))))).
%e 1,
%e 1, 1,
%e 2, 2, 1,
%e 4, 5, 3, 1,
%e 8, 12, 9, 4, 1,
%e 17, 28, 25, 14, 5, 1,
%e 33, 66, 66, 44, 20, 6, 1,
%o (Maxima)
%o T(n,i):=sum(binomial(k+i-1,i-1)*sum(binomial(k,r)*sum(binomial(r,m)*sum(binomial(j,-r+n-m-k-j-i)*binomial(m,j)*2^(-r+n-m-k-j-i),j,0,m),m,0,r),r,0,k),k,0,n-i);
%K nonn,tabl
%O 1,4
%A _Vladimir Kruchinin_, Dec 15 2011
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