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A229212 Square array of numerators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Sep 16 2013

STATUS

approved

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Last modified April 15 04:04 EDT 2021. Contains 342974 sequences. (Running on oeis4.)