A229213 Square array of denominators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.

1, 2, 4, 3, 16, 27, 4, 36, 216, 256, 5, 64, 729, 4096, 3125, 6, 100, 1728, 20736, 100000, 46656, 7, 144, 3375, 65536, 759375, 2985984, 823543, 8, 196, 5832, 160000, 3200000, 34012224, 105413504, 16777216, 9, 256

Offset: 1

Author

Jean-François Alcover, Sep 16 2013

Keywords

• frac
• tabl
• nonn

Comments

Limit(t(n,k), n -> infinity) = exp(1/k).

1st row = A000027

2nd row = A016742

3rd row = A016767

4th row = A016804

5th row = A016853

1st column = A000312

2nd column = A062971

3rd column = A091482

4th column = A091483

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 denominators begins:
1,      2,     3,     4, ...
4,     16,    36,    64, ...
27,   216,   729,  1728, ...
256, 4096, 20736, 65536, ...
...
Triangle of antidiagonals begins:
1;
2, 4;
3, 16, 27;
4, 36, 216, 256;
...
		

Crossrefs

Cf. A229212(numerators), A016742, A016767, A016804, A016853, A000312, A062971, A091482, A091483.

Programs

Mathematica

t[n_, k_] := (1+1/(k*n))^n; Table[t[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten // Denominator