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

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

Offset: 1

Author

Ralf Stephan, Feb 03 2005

Keywords

• nonn
• tabl

Examples

			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,
		

References

• A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, identity 140.

Crossrefs

Rows include A000032, A001254, A075155, A099923, A103325.

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}) ] ... ]].