OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 3*n*(3*n + 1)*(3*n + 2) = 6*binomial(3*n+2,3) = 6*A228888(n).
a(-n) = -A054776(n).
G.f.: 6*x*(10 + 16*x + x^2)/(1 - x)^4 = 60*x + 336*x^2 + 990*x^3 + ....
Sum {n >= 1} 1/a(n) = 3/4 - log(3)/4 - 1/12*sqrt(3)*Pi;
Sum {n >= 1} (-1)^n/a(n) = 3/4 - 2/3*log(2) - 1/18*sqrt(3)*Pi.
From Elmo R. Oliveira, Nov 28 2025: (Start)
E.g.f.: 3*x*(3*x + 2)*(3*x + 10)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)
MAPLE
seq(3*n*(3*n+1)*(3*n+2), n = 1..35);
MATHEMATICA
CoefficientList[Series[6 (10 + 16 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 10 2013 *)
Table[Times@@(3n+{0, 1, 2}), {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {60, 336, 990, 2184}, 40] (* Harvey P. Dale, Dec 20 2023 *)
PROG
(Magma) [3*n*(3*n+1)*(3*n+2): n in [1..40]]; // Vincenzo Librandi, Sep 10 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Sep 09 2013
STATUS
approved