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Differences of reciprocals of unity.
(Formerly M5433 N2362)
7

%I M5433 N2362 #21 Jun 13 2015 00:48:03

%S 1,274,48076,6998824,929081776,117550462624,14500866102976,

%T 1765130436471424,213373597575314176,25700650466807540224,

%U 3089923562153380965376,371145495540181143169024,44558899569395347436056576,5348360831598738338465357824

%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 Colin Barker, <a href="/A001242/b001242.txt">Table of n, a(n) for n = 1..481</a>

%H Mircea Merca, <a href="http://dx.doi.org/10.1007/s10998-014-0034-3">Some experiments with complete and elementary symmetric functions</a>, Periodica Mathematica Hungarica, 69 (2014), 182-189.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (274,-27000,1224000,-25920000,207360000).

%F G.f.: x / ((1-24*x)*(1-30*x)*(1-40*x)*(1-60*x)*(1-120*x)).

%F a(n) = (1/24) (24^n - 4*30^n + 6*40^n - 4*60^n + 120^n).

%o (PARI) Vec(1/(-207360000*x^5+25920000*x^4-1224000*x^3+27000*x^2-274*x+1) + O(x^100)) \\ _Colin Barker_, Apr 26 2015

%Y Equals 2^(n-1) * A103878(n).

%Y Right-hand column 4 in triangle A008969.

%Y Cf. a(n) = A112492(n+3, 5).

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

%E Formulae and more terms from _Ralf Stephan_, Feb 20 2005