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%I #7 Apr 30 2015 12:32:11
%S 1,1,1,3,2,1,3,7,3,1,4,12,12,4,1,4,23,28,18,5,1,4,34,66,52,25,6,1,4,
%T 49,126,143,85,33,7,1,4,64,228,328,265,128,42,8,1,4,80,372,700,701,
%U 444,182,52,9,1,4,96,573,1352,1705,1320,693,248,63
%N Triangle, read by rows, T(n,k)= Sum_{i=0..(n-k)/2} C(2*k,i)*C(n-2*i-1,k-1).
%F G.f.: (x-1)/((x^5+2*x^3+x)*y+x-1).
%e 1;
%e 1, 1;
%e 3, 2, 1;
%e 3, 7, 3, 1;
%e 4, 12, 12, 4, 1;
%e 4, 23, 28, 18, 5, 1;
%o (Maxima)
%o T(n,k):=sum(binomial(2*k,i)*binomial(n-2*i-1,k-1),i,0,(n-k)/2);
%o (PARI) T(n,k)=sum(i=0,(n-k)\2, binomial(2*k,i)*binomial(n-2*i-1,k-1)) \\ _Charles R Greathouse IV_, Apr 30 2015
%K nonn,tabl
%O 1,4
%A _Vladimir Kruchinin_, Apr 29 2015
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