A160834 Expansion of: (1+62*x+567*x^2+1068*x^3+503*x^4+54*x^5+x^6)/(1-x)^7.

1, 69, 1029, 6857, 29273, 94589, 252813, 589009, 1236913, 2394805, 4343637, 7467417, 12275849, 19429229, 29765597, 44330145, 64406881, 91552549, 127632805, 174860649, 235837113, 313594205, 411640109, 534006641, 685298961

Offset: 0

Author

N. J. A. Sloane, Nov 18 2009

Keywords

• nonn

Comments

Source: the De Loera et al. article and the Haws website listed in A160747.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Magma

[1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

Maple

A160834:=n->1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15: seq(A160834(n), n=0..30); # Wesley Ivan Hurt, Mar 04 2014

Mathematica

Table[1 + n*(n + 1)*(47*n^4 + 104*n^3 + 171*n^2 + 114*n + 74)/15, {n, 0, 30}] (* Wesley Ivan Hurt, Mar 04 2014 *)

PARI

for(n=0, 30, print1(1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n +74)/15, ", ")) \\ G. C. Greubel, Apr 28 2018

Formula

G.f.: (1+62*x+567*x^2+1068*x^3+503*x^4+54*x^5+x^6)/(1-x)^7.

a(n) = 1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15. - R. J. Mathar, Sep 17 2011

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). - Wesley Ivan Hurt, Oct 01 2021