A229212 Square array of numerators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.
2, 3, 9, 4, 25, 64, 5, 49, 343, 625, 6, 81, 1000, 6561, 7776, 7, 121, 2197, 28561, 161051, 117649, 8, 169, 4096, 83521, 1048576, 4826809, 2097152, 9, 225, 6859, 194481, 4084101, 47045881, 170859375, 43046721, 10, 289
Offset: 1
Examples
Table of fractions begins: 2, 3/2, 4/3, 5/4, ... 9/4, 25/16, 49/36, 81/64, ... 64/27, 343/216, 1000/729, 2197/1728, ... 625/256, 6561/4096, 28561/20736, 83521/65536, ... ... Table of numerators begins: 2, 3, 4, 5, ... 9, 25, 49, 81, ... 64, 343, 1000, 2197, ... 625, 6561, 28561, 83521, ... ... Triangle of antidiagonals begins: 2; 3, 9; 4, 25, 64; 5, 49, 343, 625; ...
Programs
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Mathematica
t[n_, k_] := (1+1/(k*n))^n; Table[t[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten // Numerator
Comments