A028037 -id:A028037 - cp's OEIS frontend

A001241 Differences of reciprocals of unity.

1, 50, 1660, 46760, 1217776, 30480800, 747497920, 18139003520, 437786795776, 10536798272000, 253246254177280, 6082300519393280, 146028165842661376, 3505313580591718400, 84135194495708938240, 2019336829962040279040

Offset: 1

N. J. A. Sloane

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).

Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (50, -840, 5760, -13824).

Equals 2^(n-1) * A028037(n-1).
Right-hand column 3 in triangle A008969.
a(n) = A112492(n+2, 4).

A001241:=1/(6*z-1)/(8*z-1)/(12*z-1)/(24*z-1); [Conjectured by Simon Plouffe in his 1992 dissertation.]

G.f.: x / ((1-6*x)*(1-8*x)*(1-12*x)*(1-24*x)).

a(n) = (1/6)*(-6^n + 3*8^n - 3*12^n + 24^n).

Formulae and more terms from Ralf Stephan, Feb 20 2005

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

Jean-François Alcover, May 12 2015

			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.

Cf. A257895 (denominators).

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

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

cp's OEIS Frontend

A001241 Differences of reciprocals of unity.

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