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%I #4 Mar 30 2012 18:51:35
%S 1,0,1,0,1,1,0,2,2,1,0,5,6,3,1,0,14,20,12,4,1,0,42,70,51,20,5,1,0,132,
%T 252,222,104,30,6,1,0,429,924,978,548,185,42,7,1,0,1430,3432,4338,
%U 2904,1150,300,56,8,1,0,4862,12870,19323,15432,7170,2154,455,72,9,1,0,16796
%N Square array read by antidiagonals: T(n,k)=(T(n,k-1)*n^2-Catalan(k-1)*n)/(n-1) with a(n,0)=1 and a(1,k)=Catalan(k) where Catalan(k)=C(2k,k)/(k+1)=A000108(k).
%F T(n, k) =A067345(n, k)*n =A067346(n, k)*n/(n-1)
%e Array begins
%e 1 0 0 0 0 0 0 0 ... k=0
%e 1 1 2 5 14 42 132 429 ... k=1
%e 1 2 6 20 70 252 924 3432 ... k=2
%e 1 3 12 51 222 978 4338 19323 ... k=3
%Y Rows give A000007, A000108, A000984, A007854, A076035, A076036. Columns give A000012, A001700, A002378, A062158.
%K nonn,tabl
%O 0,8
%A _Henry Bottomley_, Jan 16 2002
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