A160836 G.f.: (1+62*x+565*x^2+1050*x^3+485*x^4+52*x^5+x^6)/(1-x)^7.

1, 69, 1027, 6825, 29073, 93789, 250363, 582737, 1222801, 2366005, 4289187, 7370617, 12112257, 19164237, 29351547, 43702945, 63482081, 90220837, 125754883, 172261449, 232299313, 308851005, 405367227, 525813489, 674718961

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)*(277*n^4+629*n^3+1031*n^2+679*n+444)/90: n in [0..30]]; // Vincenzo Librandi, Sep 18 2011

Mathematica

CoefficientList[Series[(1+62x+565x^2+1050x^3+485x^4+52x^5+x^6)/(1-x)^7, {x,0,30}],x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,69,1027,6825,29073,93789,250363},30] (* Harvey P. Dale, Sep 01 2015 *)

PARI

x='x+O('x^30); Vec((1+62*x+565*x^2+1050*x^3+485*x^4+52*x^5 + x^6)/(1-x)^7) \\ G. C. Greubel, Apr 28 2018

Formula

a(n) = 1 +n*(n+1)*(277*n^4+629*n^3+1031*n^2+679*n+444)/90. - R. J. Mathar, Sep 17 2011

a(0)=1, a(1)=69, a(2)=1027, a(3)=6825, a(4)=29073, a(5)=93789, a(6)=250363, 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). - Harvey P. Dale, Sep 01 2015