A338036 Triangle T(n,m) = Sum_{k=1..m} C(2*m-k-1,m-k)*C(2*(2*m-k),n-2*m+k), n>0, m>0.

1, 2, 1, 1, 6, 1, 0, 18, 9, 1, 0, 34, 45, 12, 1, 0, 41, 164, 78, 15, 1, 0, 30, 453, 376, 120, 18, 1, 0, 12, 936, 1490, 695, 171, 21, 1, 0, 2, 1429, 4916, 3305, 1158, 231, 24, 1, 0, 0, 1596, 13266, 13647, 6333, 1792, 300, 27, 1

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

G.f.: 2*x^2*(x+1)^4/(1-4*x^2*(x+1)^4*y+(2*x*(x+1)^2-1)*sqrt(1-4*x^2*(x+1)^4*y)).

Example

1,
2,1,
1,6,1,
0,18,9,1,
0,34,45,12,1,
0,41,164,78,15,1,
0,30,453,376,120,18,1

Mathematica

T[n_, m_] := Sum[Binomial[2*m - k - 1, m - k] * Binomial[2*(2*m - k), n - 2*m + k], {k, 1, m}]; Table[T[n, m], {n, 1, 10}, {m, 1, n}] // Flatten (* Amiram Eldar, Oct 08 2020 *)

Prog

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

Crossrefs

Sequence in context: A245567 A337419 A204168 * A216914 A216917 A320637

Adjacent sequences: A338033 A338034 A338035 * A338037 A338038 A338039

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Oct 07 2020

Status

approved