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%I #9 Apr 30 2015 21:05:18
%S 1,4,1,24,8,1,172,64,12,1,1360,536,120,16,1,11444,4672,1156,192,20,1,
%T 100520,42024,11088,2096,280,24,1,911068,387456,106908,22016,3420,384,
%U 28,1,8457504,3643448,1038984,227408,39120,5192,504,32,1
%N Triangle, read by rows, T(n,k)=k/n*Sum_{i=0..n-k} C(2*n,n-k-i)*C(2*n+i-1,i).
%F G.f.: 1/(1-x*B(x)^2*y)-1, where B(x) is g.f. of A027307.
%F G.f. satisfies A(x)=x*[(1+A(x))/(1-A(x))]^2.
%e 1;
%e 4, 1;
%e 24, 8, 1;
%e 172, 64, 12, 1;
%e 1360, 536, 120, 16, 1;
%o (Maxima)
%o T(n,k):=(k*sum(binomial(2*n,n-k-i)*binomial(2*n+i-1,i),i,0,n-k))/n;
%Y Cf. A027307. First column = A032349.
%K nonn,tabl
%O 1,2
%A _Vladimir Kruchinin_, Apr 28 2015