A024184 Third elementary symmetric function of 3,4,...,n+4.

60, 342, 1175, 3135, 7140, 14560, 27342, 48150, 80520, 129030, 199485, 299117, 436800, 623280, 871420, 1196460, 1616292, 2151750, 2826915, 3669435, 4710860, 5986992, 7538250, 9410050, 11653200, 14324310, 17486217, 21208425, 25567560

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48.

If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j), then a(n-2) = -f(n,n-3,3), for n >= 3. - Milan Janjic, Dec 20 2008

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7), with a(1)=60, a(2)=342, a(3)=1175, a(4)=3135, a(5)=7140, a(6)=14560, a(7)=27342. - Harvey P. Dale, Oct 31 2011

G.f.: x*(8*x^3-41*x^2+78*x-60) / (x-1)^7. - Colin Barker, Aug 15 2014

a(n) = A000292(n) * (n+7)*(n^2+13*n+46)/8. - R. J. Mathar, Oct 01 2016

Maple

seq(n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48, n=1..40); # Muniru A Asiru, May 19 2018

Mathematica

Table[n(n+1)(n+2)(n+7)(n^2+13n+46)/48, {n, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {60, 342, 1175, 3135, 7140, 14560, 27342}, 30] (* Harvey P. Dale, Oct 31 2011 *)

Prog

(PARI) Vec(x*(8*x^3-41*x^2+78*x-60)/(x-1)^7 + O(x^100)) \\ Colin Barker, Aug 15 2014
(Magma) [n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48: n in [1..40]]; // Vincenzo Librandi, May 03 2018
(GAP) List([1..30], n->n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48); # Muniru A Asiru, May 19 2018

Crossrefs

Sequence in context: A228889 A262385 A326051 * A293615 A119631 A269048

Adjacent sequences: A024181 A024182 A024183 * A024185 A024186 A024187

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved