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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). 0

%I

%S 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 655,401,96,1,43,387,1405,2575,2541,1293,267,1,57,686,3325,8295,11711,

%U 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 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 G.f.: (x*y+x+1)/(2*sqrt((-x*y-x+1)^2-4*x*y*(x*y+x)))+1/2.

%e 1;

%e 1, 1;

%e 1, 3, 2;

%e 1, 7, 11, 5;

%e 1, 13, 36, 37, 13;

%e 1, 21, 92, 160, 123, 35;

%o (Maxima)

%o T(n,k):=sum(binomial(n-i,i)*binomial(n-i,k-i)*binomial(n-1,i),i,0,n/2);

%Y Cf. A123160.

%Y Cf. A005773 (right diagonal).

%K nonn,tabl

%O 0,5

%A _Vladimir Kruchinin_, Feb 16 2019

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Last modified June 12 19:29 EDT 2021. Contains 344960 sequences. (Running on oeis4.)