A024195 Integer part of (4th elementary symmetric function of S(n))/(3rd elementary symmetric of S(n)), where S(n) = {3,4, ..., n+5}.

1, 2, 3, 5, 7, 9, 12, 15, 18, 21, 25, 28, 32, 37, 41, 46, 51, 56, 62, 67, 73, 80, 86, 93, 100, 107, 115, 122, 130, 139, 147, 156, 165, 174, 184, 193, 203, 214, 224, 235, 246, 257

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

Conjectured g.f.: (-1-x^14+3*x^13-4*x^12+3*x^11-x^10+x^7-x^6-x^2+x)/((x^2+1)*(x^4+1)*(x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009, confirmed by Robert Israel, May 06 2018

Example

For n=1, the 4th elementary symmetric function of (3,4,5,6) is 3*4*5*6 = 360, and the 3rd elementary symmetric function of (3,4,5,6) is 3*4*5 + 3*4*6 + 3*5*6 + 4*5*6 = 342.  So 360/342 = 1.0526..., and a(1) = 1. - Michael B. Porter, May 05 2018

Maple

seq(floor(1/120* x* (53848 + 26922 *x + 5165 *x^2 + 450* x^3 + 15* x^4)/(8 + x)/(60 + 15* x + x^2)), x=1..50); # Robert Israel, May 06 2018

Mathematica

Table[Floor[1/120 x (53848 + 26922 x + 5165 x^2 + 450 x^3 + 15 x^4)/(8 + x)/(60 + 15 x + x^2)], {x, 42}] (* Ivan Neretin, May 02 2018 *)

Prog

(Python)
import math
print([math.floor(x*(53848+26922*x+5165*x**2+450*x**3+15*x**4)/(120*(8+x)*(60+15*x+x**2))) for x in range(1, 28)]) # Paul Muljadi, Apr 03 2024
(Julia)
print([floor(x*(53848+26922*x+5165*x^2+450*x^3+15*x^4)÷(120*(8+x)*(60+15*x+x^2))) for x in 1:28]) # Paul Muljadi, Apr 04 2024

Crossrefs

Sequence in context: A200049 A279984 A184017 * A071423 A211004 A062781

Adjacent sequences: A024192 A024193 A024194 * A024196 A024197 A024198

Keyword

nonn

Author

Clark Kimberling

Status

approved