A338037 - OEIS

%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