OFFSET
0,1
COMMENTS
Essentially the same as A005586.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = binomial(n + 3, 3) - (n + 3)*(n + 2)/2.
a(n) = A214292(n+2,2). - Reinhard Zumkeller, Jul 12 2012
G.f.: (x^3-4*x^2+6*x-2)/(x-1)^4. - Colin Barker, Sep 05 2012
a(n) = Sum_{i=1..n+2} i*(n-i+1). - Wesley Ivan Hurt, Sep 21 2013
From Amiram Eldar, Sep 26 2022: (Start)
Sum_{n>=3} 1/a(n) = 77/200.
Sum_{n>=3} (-1)^(n+1)/a(n) = 363/200 - 12*log(2)/5. (End)
MAPLE
seq(sum(i*(k-i+1), i=1..k+2), k=0..99); # Wesley Ivan Hurt, Sep 21 2013
MATHEMATICA
f[n_] = Binomial[n + 3, 3] - (n + 3)*(n + 2)/2; Table[f[n], {n, 0, 30}]
LinearRecurrence[{4, -6, 4, -1}, {-2, -2, 0, 5}, 50] (* Harvey P. Dale, Jul 03 2020 *)
PROG
(PARI) a(n)=(n-2)*(n+3)*(n+2)/6 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Roger L. Bagula, Jun 09 2007
EXTENSIONS
More terms from Wesley Ivan Hurt, Sep 21 2013
STATUS
approved