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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). 1
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, 1296, 32, 1, 1, 140, 3600, 216000, 20736, 7776, 64, 1, 1, 280, 176400, 72000, 12960000, 248832, 46656, 128, 1, 1, 2520, 705600, 24696000, 12960000, 777600000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..51.

Zhi-Dong Bai, Chern-Ching Chao, Hsien-Kuei Hwang and Wen-Qi Liang, On the variance of the number of maxima in random vectors and its applications, The Annals of Applied Probability 1998, Vol. 8, No. 3, 886-895.

O. E. Barndorff-Nielsen and M. Sobel, On the distribution of the number of admissible points in a vector random sample. Theory Probab. Appl. 11 249-269.

FORMULA

T(n,k) = Sum_{j=1..n} (-1)^(j-1)*j^(1-k)*binomial(n,j).

EXAMPLE

Array of fractions begins:

1,      1,          1,             1,                 1,                    1, ...

1,    3/2,        7/4,          15/8,             31/16,                63/32, ...

1,   11/6,      85/36,       575/216,         3661/1296,           22631/7776, ...

1,  25/12,    415/144,     5845/1728,       76111/20736,        952525/248832, ...

1, 137/60, 12019/3600, 874853/216000, 58067611/12960000, 3673451957/777600000, ...

1,  49/20, 13489/3600,  336581/72000, 68165041/12960000,   483900263/86400000, ...

...

Row 2 (denominators) is A000079 (powers of 2),

Row 3 is A000400 (powers of 6),

Row 4 is A001021 (powers of 12),

Row 5 is A159991,

Row 6 is not in the OEIS.

Column 2 (denominators) is A002805 (denominators of harmonic numbers),

Column 3 is A051418 (lcm(1..n)^2),

Column 4 is not in the OEIS.

MATHEMATICA

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

CROSSREFS

Cf. A257894 (numerators).

Sequence in context: A186287 A318393 A139622 * A186023 A103880 A135899

Adjacent sequences:  A257892 A257893 A257894 * A257896 A257897 A257898

KEYWORD

nonn,frac,tabl

AUTHOR

Jean-Fran├žois Alcover, May 12 2015

STATUS

approved

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)