A001241 - OEIS

A001241

Differences of reciprocals of unity.
(Formerly M5301 N2305)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

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).

LINKS

Table of n, a(n) for n=1..16.

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).

FORMULA

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).

MAPLE

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

CROSSREFS

Equals 2^(n-1) * A028037(n-1).

Right-hand column 3 in triangle A008969.

a(n) = A112492(n+2, 4).

Sequence in context: A159187 A075912 A062151 * A164986 A224121 A238283