A001241 Differences of reciprocals of unity.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• 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).

Crossrefs

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

Right-hand column 3 in triangle A008969.

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

Programs

Maple

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

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).

Extensions

Formulae and more terms from Ralf Stephan, Feb 20 2005