A337991 Triangle T(n,m)= Sum_{i=1..n} C(n,i-m)*C(n+m-i,i-1)*C(n+m-i,m)/n, T(0,0)=1.

1, 1, 1, 1, 2, 1, 2, 5, 4, 1, 4, 13, 15, 7, 1, 9, 35, 52, 36, 11, 1, 21, 96, 175, 160, 75, 16, 1, 51, 267, 576, 655, 415, 141, 22, 1, 127, 750, 1869, 2541, 2030, 952, 245, 29, 1, 323, 2123, 6000, 9492, 9156, 5488, 1988, 400, 37, 1, 835, 6046, 19107, 34476, 38976, 28476, 13356, 3852, 621, 46, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

1,
1, 1,
1, 2, 1,
2, 5, 4, 1,
4, 13, 15, 7, 1,
9, 35, 52, 36, 11, 1,
21, 96, 175, 160, 75, 16, 1,
51, 267, 576, 655, 415, 141, 22, 1

Mathematica

T[0, 0] = 1; T[n_, m_] := Sum[Binomial[n, i - m] * Binomial[n + m - i, i - 1] * Binomial[n + m - i, m]/n, {i, 1, n}]; Table[T[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Amiram Eldar, Oct 06 2020 *)

Prog

(Maxima)
T(n, m):=if m=n then 1 else if n=0 then 0 else sum(binomial(n, i-m)*binomial(n+m-i, i-1)*binomial(n+m-i, m), i, 1, n)/n;

Crossrefs

Cf. A001006, A005773, A025227, A132894.

Sequence in context: A151703 A151691 A201780 * A104560 A121435 A137156

Adjacent sequences: A337988 A337989 A337990 * A337992 A337993 A337994

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Oct 06 2020

Status

approved