A024191 [ (3rd elementary symmetric function of 3,4,...,n+4)/(3+4+...+n+4) ].

5, 19, 47, 95, 170, 280, 434, 642, 915, 1265, 1705, 2249, 2912, 3710, 4660, 5780, 7089, 8607, 10355, 12355, 14630, 17204, 20102, 23350, 26975, 31005, 35469, 40397, 45820, 51770, 58280, 65384, 73117, 81515, 90615, 100455, 111074, 122512, 134810, 148010

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Cf. A115127.

Partial sums of A005586.

Programs

Mathematica

Table[n(n+1)(n^2+13n+46)/24,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{5,19,47,95,170},40] (* Harvey P. Dale, Apr 28 2014 *)
CoefficientList[Series[(5 - 6 x + 2 x^2)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 28 2014 *)

PARI

a(n) = n*(n+1)*(n^2+13*n+46)/24 \\ Charles R Greathouse IV, Oct 21 2022

Formula

a(n)=A115127(n+2, 3), n>=2.

a(n) = n*(n+1)*(n^2+13n+46)/24 =a(n-1)+A005586(n). - Henry Bottomley, Oct 25 2001

G.f.: x*(5-6*x+2*x^2)/(1-x)^5.

a(n) = floor(A024184(n)/A055998(n+2)). - R. J. Mathar, Sep 15 2009

a(1)=5, a(2)=19, a(3)=47, a(4)=95, a(5)=170, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Apr 28 2014