A159833 a(n) = n^2*(n^2 + 15)/4.

0, 4, 19, 54, 124, 250, 459, 784, 1264, 1944, 2875, 4114, 5724, 7774, 10339, 13500, 17344, 21964, 27459, 33934, 41500, 50274, 60379, 71944, 85104, 100000, 116779, 135594, 156604, 179974, 205875, 234484, 265984, 300564, 338419, 379750, 424764

Offset: 0

Author

R. J. Mathar, Apr 23 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, 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. A008488, A000292, A000332, A000217.

Programs

Magma

[n^2 * (n^2 + 15)/4: n in [0..40]]; // Vincenzo Librandi, Dec 18 2012

Maple

seq(n^2*(n^2+15)/4,n=0..80)

Mathematica

CoefficientList[Series[-x*(1 + x)*(4*x^2 - 5*x + 4)/(x-1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2012 *)
LinearRecurrence[{5,-10,10,-5,1},{0,4,19,54,124},40] (* Harvey P. Dale, May 30 2016 *)

PARI

for(n=0, 30, print1(n^2*(n^2 +15)/4, ", ")) \\ G. C. Greubel, May 19 2018

Formula

a(n) = A008488(n+1)-2 = 4 - 15*A000292(n+1) + 6*A000332(n+4) + 20*A000217(n+1) - 15*(n+1).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

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

E.g.f.: x*(16 +22*x +6*x^2 +x^3)*exp(x)/4. - G. C. Greubel, May 19 2018