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%I #5 Jun 13 2015 11:05:53
%S 1,1,2,1,5,6,14,30,6,42,140,75,132,630,630,75,429,2772,4410,1470,1430,
%T 12012,27720,17640,1470,4862,51480,162162,166320,39690,16796,218790,
%U 900900,1351350,623700,39690,58786,923780,4813380,9909900,7432425
%N 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.
%F Row sums equals A115081, which is column 0 of triangle A115080.
%e Table begins:
%e 1;
%e 1;
%e 2, 1;
%e 5, 6;
%e 14, 30, 6;
%e 42, 140, 75;
%e 132, 630, 630, 75;
%e 429, 2772, 4410, 1470;
%e 1430, 12012, 27720, 17640, 1470;
%e 4862, 51480, 162162, 166320, 39690;
%e 16796, 218790, 900900, 1351350, 623700, 39690; ...
%o (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)
%o (PARI) T(n,k)=(2*n-2*k)!*n!/k!/(n-k)!/(n-k+1)!/(n-2*k)!/2^k
%Y Cf. A115081 (row sums), A115080; A000108, A001147.
%K nonn,tabf
%O 0,3
%A _Paul D. Hanna_, Nov 19 2006
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