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

1,1

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

Links

Table of n, a(n) for n=1..38.

Example

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;
...

Mathematica

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

Crossrefs

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

Sequence in context: A329568 A249824 A227912 * A210586 A202017 A127198

Adjacent sequences: A229209 A229210 A229211 * A229213 A229214 A229215

Keyword

frac,tabl,nonn

Author

Jean-François Alcover, Sep 16 2013

Status

approved