A001242
Differences of reciprocals of unity.
Original entry on oeis.org
1, 274, 48076, 6998824, 929081776, 117550462624, 14500866102976, 1765130436471424, 213373597575314176, 25700650466807540224, 3089923562153380965376, 371145495540181143169024, 44558899569395347436056576, 5348360831598738338465357824
Offset: 1
- F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- Colin Barker, Table of n, a(n) for n = 1..481
- Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.
- Index entries for linear recurrences with constant coefficients, signature (274,-27000,1224000,-25920000,207360000).
Right-hand column 4 in triangle
A008969.
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).
Original entry on oeis.org
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
Offset: 1
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.
- 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.
-
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
Showing 1-2 of 2 results.