OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 64*Pochhammer(n/4, 3).
a(n) = n^3 + 12*n^2 + 32*n.
a(n) = [x^n] 3*x*(7*x^2 - 20*x + 15)/(x - 1)^4.
a(n) = Sum_{k=0..3} Stirling1(3, k)*(-4)^(3 - k)*n^k.
From Amiram Eldar, Oct 03 2024: (Start)
Sum_{n>=1} 1/a(n) = 1217/26880.
Sum_{n>=1} (-1)^(n+1)/a(n) = 149/8960. (End)
MAPLE
a := n -> n * (n + 4) * (n + 8): seq(a(n), n = 0..40);
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {0, 45, 120, 231}, 41] (* Hugo Pfoertner, Mar 06 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Mar 06 2024
STATUS
approved