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A298309 Triangle read by rows: T(n,m) = Sum_{i=0..n+1} C(n-i+1,i-1)*C(n-i+1,i)*C(n-i+1,m-i+1).

%I A298309 #13 Jan 22 2018 21:26:01
%S A298309 0,1,1,2,4,2,3,11,13,5,4,25,51,43,13,5,49,149,203,130,32,6,86,364,716,
%T A298309 734,382,80,7,139,787,2099,3061,2521,1105,201,8,211,1553,5385,10455,
%U A298309 12093,8311,3143,505,9,305,2851,12473,30918,47064,45075,26581,8843,1273
%N A298309 Triangle read by rows: T(n,m) = Sum_{i=0..n+1} C(n-i+1,i-1)*C(n-i+1,i)*C(n-i+1,m-i+1).
%F A298309 G.f.: ((1-(1-x*y)*(x*y+x))/sqrt((1-(x*y+1)*(x*y+x))^2-4*x*y*(x*y+x)^2)-1)/(2*x*y).
%e A298309 Triangle begins
%e A298309   0;
%e A298309   1,    1;
%e A298309   2,    4,    2;
%e A298309   3,   11,   13,    5;
%e A298309   4,   25,   51,   43,   13;
%e A298309   5,   49,  149,  203,  130,   32;
%e A298309   6,   86,  364,  716,  734,  382,   80;
%e A298309   7,  139,  787, 2099, 3061, 2521, 1105,  201;
%o A298309 (Maxima)
%o A298309 T(n,m):=sum(binomial(n-i+1,i-1)*binomial(n-i+1,i)*binomial(n-i+1,m-i+1),i,0,n+1);
%o A298309 (PARI) T(n,m) = sum(i=0, n+1, binomial(n-i+1,i-1)*binomial(n-i+1,i)*binomial(n-i+1,m-i+1));
%o A298309 tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print()); \\ _Michel Marcus_, Jan 19 2018
%Y A298309 T(n,n) is A110320(n).
%K A298309 nonn,tabl
%O A298309 0,4
%A A298309 _Vladimir Kruchinin_, Jan 17 2018