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 A103324 Square array T(n,k) read by antidiagonals: powers of Lucas numbers. 6
 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, 121, 18, 256, 1, 729, 1024, 2401, 1331, 324, 29, 512, 1, 2187, 4096, 16807, 14641, 5832, 841, 47, 1024, 1, 6561, 16384, 117649, 161051, 104976, 24389, 2209, 76 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, identity 140. LINKS FORMULA T(n, k) = A000032(k)^n, n>=1, k>=0. 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}) ] ... ]]. EXAMPLE 2,1,3,4,7,11,18, 4,1,9,16,49,121,324, 8,1,27,64,343,1331,5832, 16,1,81,256,2401,14641,104976, 32,1,243,1024,16807,161051,1889568, 64,1,729,4096,117649,1771561,34012224, CROSSREFS Rows include A000032, A001254, A075155, A099923, A103325. Sequence in context: A127554 A182319 A204182 * A221073 A181266 A302192 Adjacent sequences:  A103321 A103322 A103323 * A103325 A103326 A103327 KEYWORD nonn,tabl AUTHOR Ralf Stephan, Feb 03 2005 STATUS approved

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Last modified April 4 21:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)