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A257895 Square array read by ascending antidiagonals where T(n,k) is the mean number of maxima in a set of n random k-dimensional real vectors (denominators).

%I A257895 #12 Mar 13 2018 04:39:38
%S A257895 1,1,1,1,2,1,1,6,4,1,1,12,36,8,1,1,60,144,216,16,1,1,20,3600,1728,
%T A257895 1296,32,1,1,140,3600,216000,20736,7776,64,1,1,280,176400,72000,
%U A257895 12960000,248832,46656,128,1,1,2520,705600,24696000,12960000,777600000
%N A257895 Square array read by ascending antidiagonals where T(n,k) is the mean number of maxima in a set of n random k-dimensional real vectors (denominators).
%H A257895 Zhi-Dong Bai, Chern-Ching Chao, Hsien-Kuei Hwang and Wen-Qi Liang, <a href="https://doi.org/10.1214/aoap/1028903455">On the variance of the number of maxima in random vectors and its applications</a>, The Annals of Applied Probability 1998, Vol. 8, No. 3, 886-895.
%H A257895 O. E. Barndorff-Nielsen and M. Sobel, <a href="http://www.mathnet.ru/links/2d44785a77c46910741a6ce707ad4c3b/tvp624.pdf">On the distribution of the number of admissible points in a vector random sample.</a> Theory Probab. Appl. 11 249-269.
%F A257895 T(n,k) = Sum_{j=1..n} (-1)^(j-1)*j^(1-k)*binomial(n,j).
%e A257895 Array of fractions begins:
%e A257895 1,      1,          1,             1,                 1,                    1, ...
%e A257895 1,    3/2,        7/4,          15/8,             31/16,                63/32, ...
%e A257895 1,   11/6,      85/36,       575/216,         3661/1296,           22631/7776, ...
%e A257895 1,  25/12,    415/144,     5845/1728,       76111/20736,        952525/248832, ...
%e A257895 1, 137/60, 12019/3600, 874853/216000, 58067611/12960000, 3673451957/777600000, ...
%e A257895 1,  49/20, 13489/3600,  336581/72000, 68165041/12960000,   483900263/86400000, ...
%e A257895 ...
%e A257895 Row 2 (denominators) is A000079 (powers of 2),
%e A257895 Row 3 is A000400 (powers of 6),
%e A257895 Row 4 is A001021 (powers of 12),
%e A257895 Row 5 is A159991,
%e A257895 Row 6 is not in the OEIS.
%e A257895 Column 2 (denominators) is A002805 (denominators of harmonic numbers),
%e A257895 Column 3 is A051418 (lcm(1..n)^2),
%e A257895 Column 4 is not in the OEIS.
%t A257895 T[n_, k_] := Sum[(-1)^(j - 1)*j^(1 - k)*Binomial[n, j], {j, 1, n}]; Table[T[n - k + 1, k] // Denominator, {n, 1, 12}, {k, 1, n}] // Flatten
%Y A257895 Cf. A257894 (numerators).
%K A257895 nonn,frac,tabl
%O A257895 1,5
%A A257895 _Jean-François Alcover_, May 12 2015