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

Author

Jean-François Alcover, Sep 16 2013

Keywords

• frac
• tabl
• nonn

Comments

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

1st row = A020725

2nd row = A016754

3rd row = A016779

4th row = A016816

5th row = A016865

1st column = A000169

2nd column = A085527

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;
...
		

Crossrefs

Cf. A229213(denominators), A016754, A016779, A016816, A016865, A000169, A085527.

Programs

Mathematica

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