OFFSET
0,2
LINKS
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = A027620(n-1), n>0.
G.f.: x*(9-4*x+x^2)/(1-x)^4. - R. J. Mathar, Dec 10 2008
From Enrique Navarrete, Dec 08 2025: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n-1) = Sum_{k=2..n} A144390(k).
E.g.f.: (x^3 + 7*x^2 + 9*x)*exp(x). (End)
From Amiram Eldar, Dec 10 2025: (Start)
Sum_{n>=1} 1/a(n) = 1 - Pi^2/12.
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/2 - Pi^2/24. (End)
MATHEMATICA
Table[n(n+2)^2, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
CoefficientList[Series[x (9-4x+x^2)/(1-x)^4, {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 9, 32, 75}, 50] (* Harvey P. Dale, Aug 25 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Dec 09 2008
STATUS
approved
