A339000 Triangle T(n,m) = C(n,m)*Sum_{k=0..n} C(n,m-k)*C(n+k,k)/C(2*k,k).

1, 1, 2, 1, 7, 5, 1, 15, 32, 13, 1, 26, 111, 123, 34, 1, 40, 285, 603, 429, 89, 1, 57, 610, 2094, 2748, 1408, 233, 1, 77, 1155, 5845, 12170, 11196, 4437, 610, 1, 100, 2002, 14014, 42355, 60686, 42255, 13587, 1597, 1, 126, 3246, 30030, 124137, 254756, 271961, 150951, 40736, 4181

Offset

0,3

Links

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

Formula

G.f.: A008459(x,y)/(1-x*y*A008459(x,y)^2).

T(n,n) = Fibonacci(2*n+1).

Example

1,
1, 2,
1, 7, 5,
1, 15, 32, 13,
1, 26, 111, 123, 34,
1, 40, 285, 603, 429, 89,
1, 57, 610, 2094, 2748, 1408, 233

Prog

(Maxima)
T(n, m):=(binomial(n, m))*sum(((binomial(n, m-k))*(binomial(n+k, k)))/(binomial(2*k, k)), k, 0, n);

Crossrefs

Cf. A000045 (Fibonacci), A001519, A008459, A046748 (row sums).

Sequence in context: A143877 A319464 A019642 * A248811 A048505 A124821

Adjacent sequences: A338997 A338998 A338999 * A339001 A339002 A339003

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Nov 18 2020

Status

approved