OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
M. Hering and B. J. Howard, The ring of evenly weighted points on the line, arXiv:1211.3941 [math.AG], 2012-2014; See example 3.8.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = (n+1)*(n^2+3*n+3)*(n^2+n+1)/3. [Colin Barker, Jan 03 2013]
The formula is simpler if the offset is 1 rather than 0. For a(n) = b*(1+b^2+b^4)/3, b >= 1. - N. J. A. Sloane, Nov 12 2019
E.g.f.: exp(x)*(3 + 39*x + 96*x^2 + 66*x^3 + 15*x^4 + x^5)/3. - Stefano Spezia, Dec 22 2021
MATHEMATICA
CoefficientList[Series[(1+8x+22x^2+8x^3+x^4)/(1-x)^6, {x, 0, 40}], x] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 14, 91, 364, 1085, 2666}, 40] (* Harvey P. Dale, Jan 11 2020 *)
PROG
(PARI) a(n)=n*(9+13*n+11*n^2+5*n^3+n^4)/3+1 \\ Charles R Greathouse IV, Jan 03 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 30 2012
STATUS
approved