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%I #10 Feb 15 2023 12:04:03
%S 1,1,1,1,2,1,1,4,3,1,1,8,10,4,1,1,16,36,20,5,1,1,32,136,120,35,6,1,1,
%T 64,528,816,330,56,7,1,1,128,2080,5984,3876,792,84,8,1,1,256,8256,
%U 45760,52360,15504,1716,120,9,1,1,512,32896,357760,766480,376992,54264,3432,165,10,1
%N Square table by antidiagonals where T(n,k) = binomial(n+2^k-1,n).
%C Each column is convolution of preceding column starting from the all 1's sequence.
%F T(n,k) = Sum_{i=0..n} T(i,k-1)*T(n-i,k-1) starting with T(n,0) = 1 for n>=0.
%e Rows start:
%e 1, 1, 1, 1, 1, 1, 1,...
%e 1, 2, 4, 8, 16, 32, 64,...
%e 1, 3, 10, 36, 136, 528, 2080,...
%e 1, 4, 20, 120, 816, 5984, 45760,...
%e 1, 5, 35, 330, 3876, 52360, 766480,...
%e ...
%Y Columns include (essentially) A000012, A000027, A000292, A000580, A010968, etc. Rows include A000012, A000079, A007582, A092056.
%Y Main diagonal gives A060690.
%K nonn,tabl
%O 0,5
%A _Henry Bottomley_, Feb 19 2004
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