OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (36,-576,5376,-32256,129024,-344064,589824,-589824,262144).
FORMULA
a(n) = binomial(n+8, 8)*4^n.
G.f.: 1/(1-4*x)^9.
a(n) = A054335(n+17, 17).
a(n) = 36*a(n-1) - 576*a(n-2) + 5376*a(n-3) - 32256*a(n-4) + 129024*a(n-5) - 344064*a(n-6) + 589824*a(n-7) - 589824*a(n-8) + 262144*a(n-9). - Harvey P. Dale, Aug 30 2013
E.g.f.: (16/7!)*(315 + 10080*x + 70560*x^2 + 188160*x^3 + 235200*x^4 + 150528*x^5 + 50176*x^6 + 8192*x^7 + 512*x^8)*exp(4*x). - G. C. Greubel, Jul 21 2019
From Amiram Eldar, Mar 27 2022: (Start)
Sum_{n>=0} 1/a(n) = 704696/35 - 69984*log(4/3).
Sum_{n>=0} (-1)^n/a(n) = 2500000*log(5/4) - 11715016/21. (End)
MAPLE
seq(binomial(n+8, 8)*4^n, n=0..20); # Zerinvary Lajos, Jun 23 2008
MATHEMATICA
Table[Binomial[n+8, 8]4^n, {n, 0, 20}] (* or *) LinearRecurrence[ {36, -576, 5376, -32256, 129024, -344064, 589824, -589824, 262144}, {1, 36, 720, 10560, 126720, 1317888, 12300288, 105431040, 843448320}, 20]
PROG
(Magma) [Binomial(n+8, 8)*4^n: n in [0..20]]; // Vincenzo Librandi, May 31 2011
(PARI) vector(20, n, n--; 4^n*binomial(n+8, 8)) \\ G. C. Greubel, Jul 21 2019
(Sage) [4^n*binomial(n+8, 8) for n in (0..20)] # G. C. Greubel, Jul 21 2019
(GAP) List([0..20], n-> 4^n*Binomial(n+8, 8)); # G. C. Greubel, Jul 21 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Wolfdieter Lang, Mar 13 2000
STATUS
approved