A160767 Expansion of (1+12*x+28*x^2+12*x^3+x^4)/(1-x)^5.

1, 17, 103, 367, 971, 2131, 4117, 7253, 11917, 18541, 27611, 39667, 55303, 75167, 99961, 130441, 167417, 211753, 264367, 326231, 398371, 481867, 577853, 687517, 812101, 952901, 1111267, 1288603, 1486367, 1706071, 1949281, 2217617, 2512753

Offset: 0

Author

N. J. A. Sloane, Nov 18 2009

Keywords

• nonn
• easy

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

Magma

[(9*n^4 +18*n^3 +23*n^2 +14*n +4)/4: n in [0..30]]; // G. C. Greubel, Apr 26 2018

Mathematica

CoefficientList[Series[(1+12x+28x^2+12x^3+x^4)/(1-x)^5,{x,0,40}],x] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,17,103,367,971},40] (* Harvey P. Dale, Dec 11 2014 *)

PARI

for(n=0, 30, print1((9*n^4 +18*n^3 +23*n^2 +14*n +4)/4, ", ")) \\ G. C. Greubel, Apr 26 2018

Formula

G.f.: (1+12*x+28*x^2+12*x^3+x^4)/(1-x)^5.

a(n) = 9*n^4/4 +9*n^3/2 +23*n^2/4 +7*n/2 +1. - R. J. Mathar, Sep 11 2011

a(0)=1, a(1)=17, a(2)=103, a(3)=367, a(4)=971, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Feb 28 2015

E.g.f.: (4 + 64*x + 140*x^2 + 72*x^3 + 9*x^4)*exp(x)/4. - G. C. Greubel, Apr 26 2018