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A080420 a(n) = (n+1)*(n+6)*3^n/6. 7
1, 7, 36, 162, 675, 2673, 10206, 37908, 137781, 492075, 1732104, 6022998, 20726199, 70681653, 239148450, 803538792, 2683245609, 8910671247, 29443957164, 96855122250, 317297380491, 1035574967097, 3368233731366, 10920608743932, 35303692060125, 113819103201843 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Gregory Gerard Wojnar, Daniel Sz. Wojnar, and Leon Q. Brin, Universal peculiar linear mean relationships in all polynomials, arXiv:1706.08381 [math.GM], 2017. See p. 4.
FORMULA
G.f.: (1-2*x)/(1-3*x)^3.
From G. C. Greubel, Dec 22 2023: (Start)
a(n) = (n+6)*A288834(n)/2, for n >= 1.
a(n) = A136158(n+2, 2).
E.g.f.: (1/2)*(2 + 8*x + 3*x^2)*exp(3*x). (End)
From Amiram Eldar, Jan 11 2024: (Start)
Sum_{n>=0} 1/a(n) = 17721/50 - 4356*log(3/2)/5.
Sum_{n>=0} (-1)^n/a(n) = 4392*log(4/3)/5 - 12591/50. (End)
MATHEMATICA
CoefficientList[Series[(1 - 2 x) / (1 - 3 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)
Table[(n+1)(n+6)3^n/6, {n, 0, 30}] (* or *) LinearRecurrence[{9, -27, 27}, {1, 7, 36}, 30] (* Harvey P. Dale, Apr 02 2019 *)
PROG
(Magma) [(n+1)*(n+6)*3^n/6: n in [0..30]]; // Vincenzo Librandi, Aug 05 2013
(SageMath) [(n+1)*(n+6)*3^n/6 for n in range(31)] # G. C. Greubel, Dec 22 2023
CROSSREFS
T(n,2) in triangle A080419.
Sequence in context: A184246 A097554 A055221 * A243037 A181292 A026018
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 19 2003
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)