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Triangle read by rows: T(n,k)=(1/2)*C(n+k,k)*C(n,n-k).
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%I #7 Dec 29 2021 19:01:31

%S 1,3,3,6,15,10,10,45,70,35,15,105,280,315,126,21,210,840,1575,1386,

%T 462,28,378,2100,5775,8316,6006,1716,36,630,4620,17325,36036,42042,

%U 25740,6435,45,990,9240,45045,126126,210210,205920,109395,24310,55,1485,17160

%N Triangle read by rows: T(n,k)=(1/2)*C(n+k,k)*C(n,n-k).

%t Table[(Binomial[n+k,k]Binomial[n,n-k])/2,{n,10},{k,n}]//Flatten (* _Harvey P. Dale_, Dec 29 2021 *)

%o (PARI) T(n,k)=(1/2)*binomial(n+k,k)*binomial(n,n-k)

%Y First column = A000217, second column = A050534, main diagonal = A001700, second diagonal = A033876.

%Y Cf. A063007.

%K nonn,tabl

%O 1,2

%A _Benoit Cloitre_, Mar 20 2004

%E Definition corrected by _Harvey P. Dale_, Dec 29 2021