%I
%S 2,4,1,8,1,3,16,1,9,4,32,1,27,16,7,64,1,81,64,49,11,128,1,243,256,343,
%T 121,18,256,1,729,1024,2401,1331,324,29,512,1,2187,4096,16807,14641,
%U 5832,841,47,1024,1,6561,16384,117649,161051,104976,24389,2209,76
%N Square array T(n,k) read by antidiagonals: powers of Lucas numbers.
%D A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, identity 140.
%F T(n, k) = A000032(k)^n, n>=1, k>=0.
%F T(n, k) = Sum[i_1>=0, Sum[i_2>=0, ... Sum[i_{k1}>=0, 2^i_1*C(n, i_1)*C(ni_1, i_2)*C(ni_2, i_3)*...*C(ni_{k2}, i_{k1}) ] ... ]].
%e 2,1,3,4,7,11,18,
%e 4,1,9,16,49,121,324,
%e 8,1,27,64,343,1331,5832,
%e 16,1,81,256,2401,14641,104976,
%e 32,1,243,1024,16807,161051,1889568,
%e 64,1,729,4096,117649,1771561,34012224,
%Y Rows include A000032, A001254, A075155, A099923, A103325.
%K nonn,tabl
%O 1,1
%A _Ralf Stephan_, Feb 03 2005
