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A081139 9th binomial transform of (0,0,1,0,0,0,...). 22
0, 0, 1, 27, 486, 7290, 98415, 1240029, 14880348, 172186884, 1937102445, 21308126895, 230127770466, 2447722649502, 25701087819771, 266895911974545, 2745215094595320, 28001193964872264, 283512088894331673 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Starting at 1, the three-fold convolution of A001019 (powers of 9).
LINKS
FORMULA
a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3), a(0)=a(1)=0, a(2)=1.
a(n) = 9^(n-2)*binomial(n, 2).
G.f.: x^2/(1-9*x)^3.
E.g.f.: (x^2/2)*exp(9*x). - G. C. Greubel, May 13 2021
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=2} 1/a(n) = 18 - 144*log(9/8).
Sum_{n>=2} (-1)^n/a(n) = 180*log(10/9) - 18. (End)
MATHEMATICA
LinearRecurrence[{27, -243, 729}, {0, 0, 1}, 30] (* Harvey P. Dale, Jan 30 2018 *)
PROG
(Magma) [9^n* Binomial(n+2, 2): n in [-2..20]]; // Vincenzo Librandi, Oct 16 2011
CROSSREFS
Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), this sequence (q=9), A081140 (q=10), A081141 (q=11), A081142 (q=12), A027476 (q=15).
Cf. A001019.
Sequence in context: A026006 A024346 A025983 * A020976 A024114 A025982
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 08 2003
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)