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

1,1

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

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

Example

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

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A380071 A206341 A357495 * A006052 A105976 A340342

Adjacent sequences: A024390 A024391 A024392 * A024394 A024395 A024396

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

a(3) corrected by Neven Juric, Jun 25 2005

Status

approved