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A229212 Square array of numerators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.

%I A229212 #13 Sep 20 2013 04:29:54
%S A229212 2,3,9,4,25,64,5,49,343,625,6,81,1000,6561,7776,7,121,2197,28561,
%T A229212 161051,117649,8,169,4096,83521,1048576,4826809,2097152,9,225,6859,
%U A229212 194481,4084101,47045881,170859375,43046721,10,289
%N A229212 Square array of numerators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.
%C A229212 Limit(t(n,k), n -> infinity) = exp(1/k).
%C A229212 1st row = A020725
%C A229212 2nd row = A016754
%C A229212 3rd row = A016779
%C A229212 4th row = A016816
%C A229212 5th row = A016865
%C A229212 1st column = A000169
%C A229212 2nd column = A085527
%e A229212 Table of fractions begins:
%e A229212    2,       3/2,        4/3,         5/4, ...
%e A229212   9/4,     25/16,      49/36,       81/64, ...
%e A229212 64/27,   343/216,   1000/729,    2197/1728, ...
%e A229212 625/256, 6561/4096, 28561/20736, 83521/65536, ...
%e A229212 ...
%e A229212 Table of numerators begins:
%e A229212 2,      3,     4,     5, ...
%e A229212 9,     25,    49,    81, ...
%e A229212 64,   343,  1000,  2197, ...
%e A229212 625, 6561, 28561, 83521, ...
%e A229212 ...
%e A229212 Triangle of antidiagonals begins:
%e A229212 2;
%e A229212 3, 9;
%e A229212 4, 25, 64;
%e A229212 5, 49, 343, 625;
%e A229212 ...
%t A229212 t[n_, k_] := (1+1/(k*n))^n; Table[t[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten // Numerator
%Y A229212 Cf. A229213(denominators), A016754, A016779, A016816, A016865, A000169, A085527.
%K A229212 frac,tabl,nonn
%O A229212 1,1
%A A229212 _Jean-François Alcover_, Sep 16 2013