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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, 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 (list; graph; refs; listen; history; text; internal format)
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: A026221 A030740 A095242 * A217105 A143892 A129321

Adjacent sequences:  A125077 A125078 A125079 * A125081 A125082 A125083

KEYWORD

nonn,tabf

AUTHOR

Paul D. Hanna, Nov 19 2006

STATUS

approved

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Last modified February 20 14:37 EST 2018. Contains 299380 sequences. (Running on oeis4.)