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A306226 Triangle read by rows: T(n,k) = Sum_{i=0..n/2} C(n-i,i)*C(n-i,k-i)*C(n-1,i) (0 <= k <= n).

%I A306226 #46 Feb 16 2019 06:56:11
%S A306226 1,1,1,1,3,2,1,7,11,5,1,13,36,37,13,1,21,92,160,123,35,1,31,200,520,
%T A306226 655,401,96,1,43,387,1405,2575,2541,1293,267,1,57,686,3325,8295,11711,
%U A306226 9492,4131,750,1,73,1136,7112,23128,43736,50148,34476,13107,2123,1,91,1782,14040,57708,140112,212856,205332,122535,41353,6046
%N A306226 Triangle read by rows: T(n,k) = Sum_{i=0..n/2} C(n-i,i)*C(n-i,k-i)*C(n-1,i)  (0 <= k <= n).
%F A306226 G.f.: (x*y+x+1)/(2*sqrt((-x*y-x+1)^2-4*x*y*(x*y+x)))+1/2.
%e A306226 1;
%e A306226 1, 1;
%e A306226 1, 3, 2;
%e A306226 1, 7, 11, 5;
%e A306226 1, 13, 36, 37, 13;
%e A306226 1, 21, 92, 160, 123, 35;
%o A306226 (Maxima)
%o A306226 T(n,k):=sum(binomial(n-i,i)*binomial(n-i,k-i)*binomial(n-1,i),i,0,n/2);
%Y A306226 Cf. A123160.
%Y A306226 Cf. A005773 (right diagonal).
%K A306226 nonn,tabl
%O A306226 0,5
%A A306226 _Vladimir Kruchinin_, Feb 16 2019