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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
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
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
Sequence in context: A329568 A249824 A227912 * A210586 A202017 A127198
KEYWORD
frac,tabl,nonn
AUTHOR
STATUS
approved