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A103324 Square array T(n,k) read by antidiagonals: powers of Lucas numbers. 6


%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_{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 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

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Last modified January 20 16:46 EST 2019. Contains 319335 sequences. (Running on oeis4.)