OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 8*Pochhammer(n/2, 3).
a(n) = [x^n] 3*x*(x^2 - 4*x + 5)/(x - 1)^4.
a(n) = 3 * A077415(n + 2).
From Klaus Purath, Aug 02 2024: (Start)
a(n+1) - a(n) = A211441(n+2).
a(n) = 3*Sum_{i = 1..n} A028387(i). (End)
E.g.f.: exp(x)*x*(15 + 9*x + x^2). - Stefano Spezia, Aug 18 2024
From Amiram Eldar, Oct 03 2024: (Start)
Sum_{n>=1} 1/a(n) = 11/96.
Sum_{n>=1} (-1)^(n+1)/a(n) = 5/96. (End)
MAPLE
a := n -> n*(n + 2)*(n + 4): seq(a(n), n = 0..40);
# Using the generating function:
gf := 3*x*(x^2 - 4*x + 5)/(x - 1)^4: ser := series(gf, x, 42):
seq(coeff(ser, x, n), n = 0..40);
MATHEMATICA
Table[n(n+2)(n+4), {n, 0, 40}] (* or *) CoefficientList[Series[3*x*(x^2 - 4*x + 5)/(x - 1)^4, {x, 0, 40}], x] (* James C. McMahon, Mar 05 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Mar 05 2024
STATUS
approved