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A024393 4th elementary symmetric function of the first n+3 positive integers congruent to 2 mod 3. 0
880, 12164, 80844, 363944, 1276009, 3751209, 9668253, 22494813, 48216663, 96625243, 183045863, 330597267, 573081782, 958613782, 1554102702, 2450715342, 3770450706, 5673969126, 8369825926, 12125268386, 17278763271, 24254430695 (list; graph; refs; listen; history; text; internal format)
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

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: A190030 A118799 A206341 * A006052 A105976 A265181

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

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.