%I A103324
%S A103324 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 A103324 121,18,256,1,729,1024,2401,1331,324,29,512,1,2187,4096,16807,14641,
%U A103324 5832,841,47,1024,1,6561,16384,117649,161051,104976,24389,2209,76
%N A103324 Square array T(n,k) read by antidiagonals: powers of Lucas numbers.
%D A103324 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of 
               combinatorial proof, M.A.A. 2003, identity 140.
%F A103324 T(n, k) = A000032(k)^n, n>=1, k>=0.
%F A103324 T(n, k) = Sum[i_1>=0, Sum[i_2>=0, ... Sum[i_{k-1}>=0, 2^i_1*C(n, i_1)*C(n-i_1, 
               i_2)*C(n-i_2, i_3)*...*C(n-i_{k-2}, i_{k-1}) ] ... ]].
%e A103324 2,1,3,4,7,11,18,
%e A103324 4,1,9,16,49,121,324,
%e A103324 8,1,27,64,343,1331,5832,
%e A103324 16,1,81,256,2401,14641,104976,
%e A103324 32,1,243,1024,16807,161051,1889568,
%e A103324 64,1,729,4096,117649,1771561,34012224,
%Y A103324 Rows include A000032, A001254, A075155, A099923, A103325.
%Y A103324 Sequence in context: A112852 A121531 A127554 this_sequence A087060 A065278 
               A112931
%Y A103324 Adjacent sequences: A103321 A103322 A103323 this_sequence A103325 A103326 
               A103327
%K A103324 nonn,tabl
%O A103324 1,1
%A A103324 Ralf Stephan, Feb 03 2005