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) = -a(-n) = binomial(3*n + 1,3) = 1/6*(3*n + 1)*(3*n)*(3*n - 1).
G.f.: x*(4 + 19*x + 4*x^2)/(1 - x)^4 = 4*x + 35*x^2 + 120*x^3 + ....
Sum_{n>=1} 1/a(n) = 3*log(3) - 3.
Sum_{n>=1} (-1)^n/a(n) = 4*log(2) - 3.
E.g.f.: exp(x)*x*(8 + 27*x + 9*x^2)/2. - Stefano Spezia, Sep 20 2024
MAPLE
seq(binomial(3*n+1, 3), n = 1..38);
MATHEMATICA
Table[(Binomial[3n + 1, 3]), {n, 40}] (* Vincenzo Librandi, Sep 10 2013 *)
LinearRecurrence[{4, -6, 4, -1}, {4, 35, 120, 286}, 40] (* Harvey P. Dale, Jan 11 2015 *)
PROG
(Magma) [Binomial(3*n+1, 3): n in [1..40]]; // Vincenzo Librandi, Sep 10 2013
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Peter Bala, Sep 09 2013
STATUS
approved