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A257894 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 (numerators). 1
1, 1, 1, 1, 3, 1, 1, 11, 7, 1, 1, 25, 85, 15, 1, 1, 137, 415, 575, 31, 1, 1, 49, 12019, 5845, 3661, 63, 1, 1, 363, 13489, 874853, 76111, 22631, 127, 1, 1, 761, 726301, 336581, 58067611, 952525, 137845, 255, 1, 1, 7129, 3144919, 129973303, 68165041 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..50.

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)*C(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 (numerators) is A000225 (Mersenne numbers 2^k-1),

Row 3 is A001240 (Differences of reciprocals of unity),

Row 4 is A028037,

Row 5 is A103878,

Row 6 is not in the OEIS.

Column 2 (numerators) is A001008 (Wolstenholme numbers: numerator of harmonic number),

Column 3 is A027459,

Column 4 is A027462,

Column 5 is A072913,

Column 6 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] // Numerator, {n, 1, 12}, {k, 1, n}] // Flatten

CROSSREFS

Cf. A257895 (denominators).

Sequence in context: A120270 A243752 A113711 * A103997 A256895 A223256

Adjacent sequences:  A257891 A257892 A257893 * A257895 A257896 A257897

KEYWORD

nonn,frac,tabl

AUTHOR

Jean-Fran├žois Alcover, May 12 2015

STATUS

approved

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Last modified October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)