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A036291
a(n) = n*5^n.
8
0, 5, 50, 375, 2500, 15625, 93750, 546875, 3125000, 17578125, 97656250, 537109375, 2929687500, 15869140625, 85449218750, 457763671875, 2441406250000, 12969970703125, 68664550781250, 362396240234375, 1907348632812500, 10013580322265625, 52452087402343750
OFFSET
0,2
FORMULA
G.f.: 5*x/(1 - 5*x)^2. - Vincenzo Librandi, Sep 09 2014
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = log(5/4).
Sum_{n>=1} (-1)^(n+1)/a(n) = log(6/5). (End)
From Elmo R. Oliveira, Sep 09 2024: (Start)
E.g.f.: 5*x*exp(5*x).
a(n) = n*A000351(n) = 5*A053464(n).
a(n) = 10*a(n-1) - 25*a(n-2) for n > 1. (End)
MAPLE
g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)*n, n=0..31); # Zerinvary Lajos, Jan 09 2009
MATHEMATICA
Table[n 5^n, {n, 0, 20}] (* Vincenzo Librandi, Sep 09 2014 *)
PROG
(Magma) [n*5^n: n in [0..20]]; // Vincenzo Librandi, Sep 09 2014
CROSSREFS
Sequence in context: A301997 A227883 A227261 * A060347 A133646 A043032
KEYWORD
nonn,easy
STATUS
approved