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

0,5

Links

Table of n, a(n) for n=0..54.

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).

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000217, A001700, A253942.

Sequence in context: A122831 A019701 A134813 * A164107 A093755 A176276

Adjacent sequences: A338034 A338035 A338036 * A338038 A338039 A338040

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Oct 08 2020

Status

approved