A338035 Triangle T(n,m) = (1/m)*Sum_{k=1..m} k*C(2*m-k-1,m-k)*C(2*(2*m-k),n-2*m+k), n>0, m>0.

1, 2, 1, 1, 5, 1, 0, 12, 8, 1, 0, 19, 33, 11, 1, 0, 21, 96, 63, 14, 1, 0, 15, 217, 256, 102, 17, 1, 0, 6, 386, 830, 524, 150, 20, 1, 0, 1, 533, 2241, 2147, 927, 207, 23, 1, 0, 0, 560, 5079, 7440, 4541, 1492, 273, 26, 1

Offset

1,2

Links

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

Formula

G.f.: 1/(1-(1-sqrt(x*(-4*x^5-16*x^4-24*x^3-16*x^2-4*x)*y+1))/(2*x^3+4*x^2+2*x)).

Example

1,
2,1,
1,5,1,
0,12,8,1,
0,19,33,11,1,
0,21,96,63,14,1,
0,15,217,256,102,17,1

Mathematica

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

Prog

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

Crossrefs

Cf. A338036, A338037.

Sequence in context: A231622 A165623 A264878 * A110243 A169950 A088347

Adjacent sequences: A338032 A338033 A338034 * A338036 A338037 A338038

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Oct 07 2020

Status

approved