A338037 Triangle T(n,m) = C(2*m-1,m)*C(n+2*m-1,n-m).

1, 0, 1, 0, 3, 3, 0, 6, 18, 10, 0, 10, 63, 90, 35, 0, 15, 168, 450, 420, 126, 0, 21, 378, 1650, 2730, 1890, 462, 0, 28, 756, 4950, 12740, 15120, 8316, 1716, 0, 36, 1386, 12870, 47775, 85680, 79002, 36036, 6435, 0, 45, 2376, 30030, 152880, 385560, 526680, 396396, 154440, 24310

Offset: 0

Author

Vladimir Kruchinin, Oct 08 2020

Keywords

• nonn
• tabl

Examples

			1,
0, 1,
0, 3, 3,
0, 6, 18, 10,
0, 10, 63, 90, 35,
0, 15, 168, 450, 420, 126,
0, 21, 378, 1650, 2730, 1890, 462
		

Crossrefs

Cf. A000217, A001700, A253942.

Programs

Mathematica

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 *)

Maxima

T(n,m):=binomial(2*m-1,m)*binomial(n+2*m-1,n-m);

Formula

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).