OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = binomial(n+8,3) - 2*binomial(n+8,2). - Zerinvary Lajos, Nov 25 2006, corrected by R. J. Mathar, Mar 15 2011
G.f.: x*(12 - 18*x + 7*x^2) /(x-1)^4. - R. J. Mathar, Mar 15 2011
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 27 2012
E.g.f.: (x/6)*(72 + 18*x + x^2)*exp(x). - G. C. Greubel, Jul 30 2022
From Amiram Eldar, Jul 30 2024: (Start)
Sum_{n>=1} 1/a(n) = 1443/7840.
Sum_{n>=1} (-1)^(n+1)/a(n) = 12*log(2)/7 - 1767/1568. (End)
MATHEMATICA
Table[n(n+7)(n+8)/6, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
CoefficientList[Series[x*(12-18*x+7*x^2)/(x-1)^4, {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 12, 30, 55}, 40] (* Vincenzo Librandi, Jun 27 2012 *)
PROG
(Magma) I:=[0, 12, 30, 55]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 27 2012
(PARI) a(n)=n*(n+7)*(n+8)/6 \\ Charles R Greathouse IV, Oct 16 2015
(SageMath) [n*(n+7)*(n+8)/6 for n in (0..50)] # G. C. Greubel, Jul 30 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 11 2005
STATUS
approved