A081138 8th binomial transform of (0,0,1,0,0,0, ...).

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).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (24,-192,512).

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

Adjacent sequences: A081135 A081136 A081137 * A081139 A081140 A081141

Keyword

easy,nonn

Author

Paul Barry, Mar 08 2003

Status

approved