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A229213 Square array of denominators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.

%I A229213 #10 Sep 20 2013 04:30:51
%S A229213 1,2,4,3,16,27,4,36,216,256,5,64,729,4096,3125,6,100,1728,20736,
%T A229213 100000,46656,7,144,3375,65536,759375,2985984,823543,8,196,5832,
%U A229213 160000,3200000,34012224,105413504,16777216,9,256
%N A229213 Square array of denominators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.
%C A229213 Limit(t(n,k), n -> infinity) = exp(1/k).
%C A229213 1st row = A000027
%C A229213 2nd row = A016742
%C A229213 3rd row = A016767
%C A229213 4th row = A016804
%C A229213 5th row = A016853
%C A229213 1st column = A000312
%C A229213 2nd column = A062971
%C A229213 3rd column = A091482
%C A229213 4th column = A091483
%e A229213 Table of fractions begins:
%e A229213    2,       3/2,        4/3,         5/4, ...
%e A229213   9/4,     25/16,      49/36,       81/64, ...
%e A229213 64/27,   343/216,   1000/729,    2197/1728, ...
%e A229213 625/256, 6561/4096, 28561/20736, 83521/65536, ...
%e A229213 ...
%e A229213 Table of denominators begins:
%e A229213 1,      2,     3,     4, ...
%e A229213 4,     16,    36,    64, ...
%e A229213 27,   216,   729,  1728, ...
%e A229213 256, 4096, 20736, 65536, ...
%e A229213 ...
%e A229213 Triangle of antidiagonals begins:
%e A229213 1;
%e A229213 2, 4;
%e A229213 3, 16, 27;
%e A229213 4, 36, 216, 256;
%e A229213 ...
%t A229213 t[n_, k_] := (1+1/(k*n))^n; Table[t[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten // Denominator
%Y A229213 Cf. A229212(numerators), A016742, A016767, A016804, A016853, A000312, A062971, A091482, A091483.
%K A229213 frac,tabl,nonn
%O A229213 1,2
%A A229213 _Jean-François Alcover_, Sep 16 2013