login
A036294
a(n) = n*8^n.
3
0, 8, 128, 1536, 16384, 163840, 1572864, 14680064, 134217728, 1207959552, 10737418240, 94489280512, 824633720832, 7146825580544, 61572651155456, 527765581332480, 4503599627370496, 38280596832649216, 324259173170675712, 2738188573441261568, 23058430092136939520
OFFSET
0,2
FORMULA
From Vincenzo Librandi, Aug 09 2017: (Start)
G.f.: 8*x/(8*x-1)^2.
a(n) = 16*a(n-1) - 64*a(n-2) for n > 1. (End)
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = log(8/7).
Sum_{n>=1} (-1)^(n+1)/a(n) = log(9/8). (End)
From Elmo R. Oliveira, Sep 09 2024: (Start)
E.g.f.: 8*x*exp(8*x).
a(n) = n*A001018(n) = 8*A053539(n). (End)
MATHEMATICA
Table[n 7^n, {n, 0, 30}] (* or *) LinearRecurrence[{16, -64}, {0, 8}, 31] (* Vincenzo Librandi, Aug 09 2017 *)
PROG
(Magma) [n*8^n: n in [0..20]]; // Vincenzo Librandi, Aug 09 2017
CROSSREFS
Sequence in context: A242355 A305519 A316956 * A298966 A299736 A133680
KEYWORD
nonn,easy
STATUS
approved