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A024393
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4th elementary symmetric function of the first n+3 positive integers congruent to 2 mod 3.
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3
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880, 12164, 80844, 363944, 1276009, 3751209, 9668253, 22494813, 48216663, 96625243, 183045863, 330597267, 573081782, 958613782, 1554102702, 2450715342, 3770450706, 5673969126, 8369825926, 12125268386, 17278763271, 24254430695
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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MAPLE
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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
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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a(3) corrected by Neven Juric, Jun 25 2005
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STATUS
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approved
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