A111396 a(n) = n*(n+7)*(n+8)/6.

0, 12, 30, 55, 88, 130, 182, 245, 320, 408, 510, 627, 760, 910, 1078, 1265, 1472, 1700, 1950, 2223, 2520, 2842, 3190, 3565, 3968, 4400, 4862, 5355, 5880, 6438, 7030, 7657, 8320, 9020, 9758, 10535, 11352, 12210, 13110, 14053, 15040, 16072, 17150, 18275, 19448

Offset: 0

Author

N. J. A. Sloane, Nov 11 2005

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A111373.

Programs

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

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 *)

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

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)