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%I #19 Nov 14 2018 09:29:05
%S 880,12164,80844,363944,1276009,3751209,9668253,22494813,48216663,
%T 96625243,183045863,330597267,573081782,958613782,1554102702,
%U 2450715342,3770450706,5673969126,8369825926,12125268386,17278763271,24254430695
%N 4th elementary symmetric function of the first n+3 positive integers congruent to 2 mod 3.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: -x*(x^4+332*x^3+3048*x^2+4244*x+880) / (x-1)^9. - _Colin Barker_, Aug 15 2014
%F a(n) = n*(n+1)*(n+2)*(n+3)*(405*n^4+4590*n^3+18495*n^2+30534*n+16376)/1920. - _Robert Israel_, Aug 15 2014
%e sigma_4(2,5,8,11,14,17) = 2*5*8*11 + 2*5*8*14 + 2*5*8*17 + 2*5*11*14 + 2*5*11*17 + 2*5*14*17 + 2*8*11*14 + 2*8*11*17 + 2*8*14*17 + 2*11*14*17 + 5*8*11*14 + 5*8*11*17 + 5*8*14*17 + 5*11*14*17 + 8*11*14*17 = 80844. This is also the value of n(n+1)(n+2)(n+3)(16376+30534*n+18495*n^2+4590*n^3+405*n^4)/1920 for n=3. - Neven Juric (neven.juric(AT)apis-it.hr), Jun 25 2005
%p seq(n*(n+1)*(n+2)*(n+3)*(405*n^4+4590*n^3+18495*n^2+30534*n+16376)/1920,n=0..30); # _Robert Israel_, Aug 15 2014
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{880,12164,80844,363944,1276009,3751209,9668253,22494813,48216663},30] (* _Harvey P. Dale_, Nov 14 2018 *)
%o (PARI) Vec(-x*(x^4+332*x^3+3048*x^2+4244*x+880)/(x-1)^9 + O(x^100)) \\ _Colin Barker_, Aug 15 2014
%K nonn,easy
%O 1,1
%A _Clark Kimberling_
%E a(3) corrected by Neven Juric, Jun 25 2005
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