A256640 Triangle read by rows: T(n,k) = Sum_{i=n-k..n} C(k-1,n-i)*C(i,n-k)*C(2*i,i)/(i+1).

1, 1, 1, 2, 4, 3, 5, 15, 19, 10, 14, 56, 99, 90, 36, 42, 210, 476, 603, 427, 137, 132, 792, 2190, 3536, 3507, 2032, 543, 429, 3003, 9801, 19185, 24251, 19800, 9702, 2219, 1430, 11440, 43043, 98890, 151295, 157716, 109520, 46472, 9285, 4862, 43758

Offset

0,4

Links

Table of n, a(n) for n=0..46.

Formula

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

Example

1;
1, 1;
2, 4, 3;
5, 15, 19, 10;
14, 56, 99, 90, 36;
42, 210, 476, 603, 427, 137;

Mathematica

T[n_, k_] := SeriesCoefficient[1-Sqrt[1-4*(x/(1-x)+y)]/(2*(x/(1-x)+y)), {x, 0, n}, {y, 0, k}]; Table[T[n-k, k], {n, 0, 9}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Apr 13 2015 *)

Prog

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

Crossrefs

Cf. A000108 (first column), A002212 (right diagonal).

Sequence in context: A073944 A072937 A343312 * A239466 A129509 A341844

Adjacent sequences: A256637 A256638 A256639 * A256641 A256642 A256643

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 10 2015

Status

approved