%I
%S 2,0,2,2,1,2,0,1,2,2,2,2,2,3,2,0,1,2,7,4,2,2,1,2,18,14,5,2,0,2,2,
%T 47,52,23,6,2,2,1,2,123,194,110,34,7,2,0,1,2,322,724,527,198,47,8,2,
%U 2,2,2,843,2702,2525,1154,322,62,9,2,0,1,2,2207,10084,12098,6726,2207,488,79,10,2,2,1,2,5778,37634,57965,39202
%N Table by antidiagonals where T(n,k)=n*T(n,k1)T(n,k2) with T(n,0)=2 and T(n,1)=n.
%F For all m, T(n, k) = T(n, m)*T(n, k  m)  T(n, k  2m). T(n, 2k) = T(n, k)^2  2; T(n, 2k + 1) = T(n, k)*T(n, k + 1)  n. T(n, 3k) = T(n, k)^3  3*T(n, k); T(n, 4k) = T(n, k)^4  4*T(n, k)^2 + 2; T(n, 5k) = T(n, k)^5  5*T(n, k)^3 + 5*T(n, k) etc.
%F T(n,  k) = T(n, k); T(  n, k) = T(  n,  k) = T(n, k)*(  1)^k. T(n, k) = {n*[{((n + sqrt(n^2  4))/2)^k}  {((n  sqrt(n^2  4))/2)^k} ]  2*[{((n + sqrt(n^2  4))/2)^(k  1)}  {((n  sqrt(n^2  4))/2)^(k  1)} ]}/[sqrt(n^2  4) ].
%e Rows start (2, 0, 2, 0, 2, 0, 2,...), (2, 1, 1, 2, 1, 1, 2,...), 2, 2, 2, 2, 2, 2, 2,...), (2, 3, 7, 18, 47, 123, 322,...), (2, 4, 14, 52, 194, 724, 2702,...), ...
%Y Rows include A057079, A007395, A005248, A003500, A003501, A003499, A056854, A056918. Columns include A007395, A001477, A008865, A058794.
%K sign,tabl
%O 0,1
%A _Henry Bottomley_, May 09 2001
