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%I M5301 N2305 #33 Jun 25 2023 02:31:54
%S 1,50,1660,46760,1217776,30480800,747497920,18139003520,437786795776,
%T 10536798272000,253246254177280,6082300519393280,146028165842661376,
%U 3505313580591718400,84135194495708938240,2019336829962040279040
%N Differences of reciprocals of unity.
%D F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Mircea Merca, <a href="https://www.researchgate.net/publication/264664262_Some_experiments_with_complete_and_elementary_symmetric_functions">Some experiments with complete and elementary symmetric functions</a>, Periodica Mathematica Hungarica, 69 (2014), 182-189.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (50, -840, 5760, -13824).
%F G.f.: x / ((1-6*x)*(1-8*x)*(1-12*x)*(1-24*x)).
%F a(n) = (1/6)*(-6^n + 3*8^n - 3*12^n + 24^n).
%p A001241:=1/(6*z-1)/(8*z-1)/(12*z-1)/(24*z-1); [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]
%Y Equals 2^(n-1) * A028037(n-1).
%Y Right-hand column 3 in triangle A008969.
%Y a(n) = A112492(n+2, 4).
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E Formulae and more terms from _Ralf Stephan_, Feb 20 2005
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