A338397 Triangle read by rows: T(n,m)= Sum_{k=0..m/2} C(n-k,m-2*k)*C(n-k,m-k)*C(n,k)/C(2*k,k).

1, 1, 1, 1, 4, 2, 1, 9, 12, 4, 1, 16, 42, 34, 8, 1, 25, 110, 160, 90, 16, 1, 36, 240, 550, 540, 226, 32, 1, 49, 462, 1540, 2310, 1666, 546, 64, 1, 64, 812, 3724, 7910, 8596, 4802, 1282, 128, 1, 81, 1332, 8064, 23058, 34986, 29190, 13140, 2946, 256

Offset

0,5

Links

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

Formula

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

Example

1,
1, 1,
1, 4, 2,
1, 9, 12, 4,
1, 16, 42, 34, 8,
1, 25, 110, 160, 90, 16,
1, 36, 240, 550, 540, 226, 32

Prog

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

Crossrefs

Cf. A001263, A008459, A176280 (row sums), A338372.

Sequence in context: A208612 A183157 A211957 * A063983 A367178 A259985

Adjacent sequences: A338394 A338395 A338396 * A338398 A338399 A338400

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Oct 23 2020

Status

approved