A160765 Expansion of (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.

1, 18, 112, 403, 1071, 2356, 4558, 8037, 13213, 20566, 30636, 44023, 61387, 83448, 110986, 144841, 185913, 235162, 293608, 362331, 442471, 535228, 641862, 763693, 902101, 1058526, 1234468, 1431487, 1651203, 1895296, 2165506, 2463633, 2791537

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).

Crossrefs

Cf. A000566, A002061.

Programs

Magma

[(n^2+n+1)*(5*n^2+5*n+2)/2: n in [0..40]] // Bruno Berselli, Jul 31 2015

Mathematica

Table[(n^2 + n + 1) (5 n^2 + 5 n + 2)/2, {n, 0, 40}] (* Bruno Berselli, Jul 31 2015 *)

PARI

for(n=0,30, print1((n^2+n+1)*(5*n^2+5*n+2)/2, ", ")) \\ G. C. Greubel, Apr 26 2018

Sage

[(n^2+n+1)*(5*n^2+5*n+2)/2 for n in (0..40)] # Bruno Berselli, Jul 31 2015

Formula

G.f.: (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.

a(n) = (n^2+n+1)*(5*n^2+5*n+2)/2. - R. J. Mathar, Sep 11 2011

a(n) = A000566(A002061(n+1)). - Bruno Berselli, Jul 31 2015

E.g.f.: (1/2)*(5*x^4 + 40*x^3 + 77*x^2 + 34*x + 2)*exp(x). - G. C. Greubel, Apr 26 2018