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