A220892 G.f.: (1+8*x+22*x^2+8*x^3+x^4)/(1-x)^6.

1, 14, 91, 364, 1085, 2666, 5719, 11096, 19929, 33670, 54131, 83524, 124501, 180194, 254255, 350896, 474929, 631806, 827659, 1069340, 1364461, 1721434, 2149511, 2658824, 3260425, 3966326, 4789539, 5744116, 6845189, 8109010, 9552991, 11195744, 13057121, 15158254, 17521595, 20170956, 23131549

Offset: 0

Author

N. J. A. Sloane, Dec 30 2012

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A220893.

Programs

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 *)

PARI

a(n)=n*(9+13*n+11*n^2+5*n^3+n^4)/3+1 \\ Charles R Greathouse IV, Jan 03 2013

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