A160787 G.f.: (21+104*x+103*x^2+23*x^3+x^4)/(1-x)^5.

21, 209, 938, 2833, 6771, 13881, 25544, 43393, 69313, 105441, 154166, 218129, 300223, 403593, 531636, 688001, 876589, 1101553, 1367298, 1678481, 2040011, 2457049, 2935008, 3479553, 4096601, 4792321, 5573134, 6445713, 7416983

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

[(63*n^4 + 247*n^3 +441*n^2 + 377*n + 126)/6: n in [0..30]]; // G. C. Greubel, Apr 26 2018

Mathematica

CoefficientList[Series[(21+104x+103x^2+23x^3+x^4)/ (1-x)^5, {x,0,40}], x]  (* Harvey P. Dale, Mar 28 2011 *)
LinearRecurrence[{5,-10,10,-5,1}, {21, 209, 938, 2833, 6771}, 50] (* G. C. Greubel, Apr 26 2018 *)

PARI

for(n=0,30, print1((63*n^4 + 247*n^3 +441*n^2 + 377*n + 126)/6, ", ")) \\ G. C. Greubel, Apr 26 2018

Formula

a(n) = 21*n^4/2 +247*n^3/6 +147*n^2/2 +377*n/6 +21. - R. J. Mathar, Sep 11 2011

E.g.f.: (126 + 1128*x + 1623*x^2 + 625*x^3 + 63*x^4)* exp(x)/6. - G. C. Greubel, Apr 26 2018