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%I #14 Oct 14 2020 11:10:39
%S 1,0,1,0,3,3,0,6,18,10,0,10,63,90,35,0,15,168,450,420,126,0,21,378,
%T 1650,2730,1890,462,0,28,756,4950,12740,15120,8316,1716,0,36,1386,
%U 12870,47775,85680,79002,36036,6435,0,45,2376,30030,152880,385560,526680,396396,154440,24310
%N Triangle T(n,m) = C(2*m-1,m)*C(n+2*m-1,n-m).
%F G.f.: 1+(2*x*y)/((x-1)^(3/2)*sqrt(4*x*y+x^3-3*x^2+3*x-1)-4*x*y-x^3+3*x^2-3*x+1).
%e 1,
%e 0, 1,
%e 0, 3, 3,
%e 0, 6, 18, 10,
%e 0, 10, 63, 90, 35,
%e 0, 15, 168, 450, 420, 126,
%e 0, 21, 378, 1650, 2730, 1890, 462
%t T[n_, m_] := Binomial[2*m - 1, m] * Binomial[n + 2*m - 1, n - m]; Table[T[n, m], {n, 0, 9}, {m, 0, n}] // Flatten (* _Amiram Eldar_, Oct 08 2020 *)
%o (Maxima)
%o T(n,m):=binomial(2*m-1,m)*binomial(n+2*m-1,n-m);
%Y Cf. A000217, A001700, A253942.
%K nonn,tabl
%O 0,5
%A _Vladimir Kruchinin_, Oct 08 2020
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