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A339028 Triangle T(n,m) = 3*(m+1)*C(n+m+3,m)*C(2*n+2,n-m)/((n+m+3)*C(n+1,m)).

%I A339028 #12 Dec 10 2023 17:31:27
%S A339028 1,3,3,9,12,9,28,42,42,28,90,144,162,144,90,297,495,594,594,495,297,
%T A339028 1001,1716,2145,2288,2145,1716,1001,3432,6006,7722,8580,8580,7722,
%U A339028 6006,3432,11934,21216,27846,31824,33150,31824,27846,21216,11934,41990,75582,100776,117572,125970,125970,117572,100776,75582,41990
%N A339028 Triangle T(n,m) = 3*(m+1)*C(n+m+3,m)*C(2*n+2,n-m)/((n+m+3)*C(n+1,m)).
%F A339028 G.f. ((sqrt(1-4*x*y)-sqrt(1-4*x))/(2*(x-x*y)))^3.
%e A339028 1,
%e A339028 3,3,
%e A339028 9,12,9,
%e A339028 28,42,42,28,
%e A339028 90,144,162,144,
%e A339028 90,297,495,594,594,495,297
%o A339028 (Maxima)
%o A339028 T(n,m):=if n<m then 0 else (3*(m+1)*(binomial(n+m+3,m))*(binomial(2*n+2,n-m)))/((n+m+3)*(binomial(n+1,m)));
%Y A339028 Cf. A000108, A000245, A002057 (row sums), A168256, A120406,
%K A339028 nonn,tabl
%O A339028 0,2
%A A339028 _Vladimir Kruchinin_, Nov 20 2020