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URL: https://oeis.org/A152619

⇱ A152619 - OEIS

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A152619
a(n) = n*(n+2)^2.
3
0, 9, 32, 75, 144, 245, 384, 567, 800, 1089, 1440, 1859, 2352, 2925, 3584, 4335, 5184, 6137, 7200, 8379, 9680, 11109, 12672, 14375, 16224, 18225, 20384, 22707, 25200, 27869, 30720, 33759, 36992, 40425, 44064, 47915, 51984, 56277, 60800, 65559, 70560, 75809
OFFSET
0,2
LINKS
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
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
Sequence in context: A155098 A063134 A027620 * A051662 A326247 A362526
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Dec 09 2008
STATUS
approved