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A081138
8th binomial transform of (0,0,1,0,0,0, ...).
19
0, 0, 1, 24, 384, 5120, 61440, 688128, 7340032, 75497472, 754974720, 7381975040, 70866960384, 670014898176, 6253472382976, 57724360458240, 527765581332480, 4785074604081152, 43065671436730368, 385057768140177408
OFFSET
0,4
COMMENTS
Starting at 1, the three-fold convolution of A001018 (powers of 8).
FORMULA
a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3) for n>2, a(0)=a(1)=0, a(2)=1.
a(n) = 8^(n-2)*binomial(n, 2).
G.f.: x^2/(1 - 8*x)^3.
E.g.f.: (x^2/2)*exp(8*x). - G. C. Greubel, May 13 2021
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=2} 1/a(n) = 16 - 112*log(8/7).
Sum_{n>=2} (-1)^n/a(n) = 144*log(9/8) - 16. (End)
MATHEMATICA
LinearRecurrence[{24, -192, 512}, {0, 0, 1}, 30] (* Harvey P. Dale, Jun 08 2014 *)
PROG
(Magma) [8^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), this sequence (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), A081142 (q=12), A027476 (q=15).
Sequence in context: A059157 A228406 A087292 * A269181 A266185 A114631
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 08 2003
STATUS
approved