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, 48465190981305852952576, 1163177877254362382336000

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

Paolo Xausa, Table of n, a(n) for n = 1..700

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.]

Mathematica

A001241[n_] := (-6^n + 3*8^n - 3*12^n + 24^n)/6; Array[A001241, 20] (* Paolo Xausa, May 29 2026 *)

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

Adjacent sequences: A001238 A001239 A001240 * A001242 A001243 A001244

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

Formulae and more terms from Ralf Stephan, Feb 20 2005

More terms from Paolo Xausa, May 29 2026

Status

approved