A036291 a(n) = n*5^n.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (10,-25).

Crossrefs

Cf. A000351, A053464.

Programs

Magma

[n*5^n: n in [0..20]]; // Vincenzo Librandi, Sep 09 2014

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 *)

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)