A125080 Triangle, read by rows, defined by T(n,k) = A000108(n-k)*A001147(k)*C(n,2*k), for k=0..[n/2], n>=0, where A000108 is the Catalan numbers and A001147 is the double factorials.

1, 1, 2, 1, 5, 6, 14, 30, 6, 42, 140, 75, 132, 630, 630, 75, 429, 2772, 4410, 1470, 1430, 12012, 27720, 17640, 1470, 4862, 51480, 162162, 166320, 39690, 16796, 218790, 900900, 1351350, 623700, 39690, 58786, 923780, 4813380, 9909900, 7432425

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Formula

Row sums equals A115081, which is column 0 of triangle A115080.

Example

Table begins:
1;
1;
2, 1;
5, 6;
14, 30, 6;
42, 140, 75;
132, 630, 630, 75;
429, 2772, 4410, 1470;
1430, 12012, 27720, 17640, 1470;
4862, 51480, 162162, 166320, 39690;
16796, 218790, 900900, 1351350, 623700, 39690; ...

Prog

(PARI) T(n, k)=binomial(2*n-2*k, n-k)/(n-k+1)*binomial(2*k, k)*k!/2^k*binomial(n, 2*k)
(PARI) T(n, k)=(2*n-2*k)!*n!/k!/(n-k)!/(n-k+1)!/(n-2*k)!/2^k

Crossrefs

Cf. A115081 (row sums), A115080; A000108, A001147.

Sequence in context: A325279 A095242 A357179 * A349015 A217105 A143892

Adjacent sequences: A125077 A125078 A125079 * A125081 A125082 A125083

Keyword

nonn,tabf

Author

Paul D. Hanna, Nov 19 2006

Status

approved