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%I #8 Sep 08 2013 13:30:04
%S 1,2,1,5,3,1,14,10,4,1,42,35,17,5,1,132,126,74,26,6,1,429,462,326,137,
%T 37,7,1,1430,1716,1446,726,230,50,8,1,4862,6435,6441,3858,1434,359,65,
%U 9,1,16796,24310,28770,20532,8952,2582,530,82,10,1,58786,92378,128750
%N Square array read by antidiagonals: T(n,k)=(T(n,k-1)*n^2-Catalan(k-1))/(n-1) with a(n,1)=1 and a(1,k)=Catalan(k) where Catalan(k)=C(2k,k)/(k+1)=A000108(k).
%C Also table given by Sum_{k, 0<=k<=n}A039598(n,k)*x^k ; table begins : x=0 : 1, 2, 5, 42, 132, ...(see A000108); x=1 : 1, 3, 10, 35, 126, ...(see A001700); x=2 : 1, 4, 17, 74, 326, ...(see A049027); x=3 : 1, 5, 26, 137, 726, ...(see A075025); x=4 : 1, 6, 37, 230, 1434, ...(see A075026); x=5 : 1, 7, 50, 359, 2582, ... - _Philippe Deléham_, Mar 21 2007
%F T(n, k) =A067346(n, k)/(n-1) =A067347(n, k)/n
%Y Rows include A000108, A001700, A049027. Columns essentially include A000012, A000027, A002522.
%K nonn,tabl
%O 1,2
%A _Henry Bottomley_, Jan 16 2002
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