A196280 a(n) = binomial(n+9, 9)*8^n.
1, 80, 3520, 112640, 2928640, 65601536, 1312030720, 23991418880, 407854120960, 6525665935360, 99190122217472, 1442765414072320, 20198715797012480, 273459536944168960, 3594039628409077760, 46003707243636195328, 575046340545452441600, 7035861107850241638400
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..400
- Index entries for linear recurrences with constant coefficients, signature (80,-2880,61440,-860160,8257536,-55050240,251658240,-754974720,1342177280,-1073741824).
Programs
-
Magma
[Binomial(n+9, 9)*8^n: n in [0..20]];
-
Mathematica
Table[Binomial[n+9,9]8^n,{n,0,20}] (* or *) LinearRecurrence[{80,-2880,61440,-860160,8257536,-55050240,251658240,-754974720,1342177280,-1073741824},{1,80,3520,112640,2928640,65601536,1312030720,23991418880,407854120960,6525665935360},20] (* Harvey P. Dale, May 13 2017 *)
Formula
a(n) = C(n+9,9)*8^n.
G.f.: 1 / (8*x-1)^10 . - R. J. Mathar, Oct 13 2011
From Amiram Eldar, Feb 17 2023: (Start)
Sum_{n>=0} 1/a(n) = 415065672*log(8/7) - 277121481/5.
Sum_{n>=0} (-1)^n/a(n) = 3099363912*log(9/8) - 12776837121/35. (End)