A024393 4th elementary symmetric function of the first n+3 positive integers congruent to 2 mod 3.
880, 12164, 80844, 363944, 1276009, 3751209, 9668253, 22494813, 48216663, 96625243, 183045863, 330597267, 573081782, 958613782, 1554102702, 2450715342, 3770450706, 5673969126, 8369825926, 12125268386, 17278763271, 24254430695
Offset: 1
Examples
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
Links
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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Maple
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
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Mathematica
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 *) -
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
Formula
G.f.: -x*(x^4+332*x^3+3048*x^2+4244*x+880) / (x-1)^9. - Colin Barker, Aug 15 2014
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
Extensions
a(3) corrected by Neven Juric, Jun 25 2005