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A229213
Square array of denominators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.
1
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
1,2
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
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 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;
...
MATHEMATICA
t[n_, k_] := (1+1/(k*n))^n; Table[t[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten // Denominator
CROSSREFS
KEYWORD
frac,tabl,nonn
AUTHOR
STATUS
approved