A064751 a(n) = n*5^n - 1.

4, 49, 374, 2499, 15624, 93749, 546874, 3124999, 17578124, 97656249, 537109374, 2929687499, 15869140624, 85449218749, 457763671874, 2441406249999, 12969970703124, 68664550781249, 362396240234374, 1907348632812499, 10013580322265624, 52452087402343749, 274181365966796874

Offset: 1

Author

N. J. A. Sloane, Oct 19 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 1..150
• Paul Leyland, Factors of Cullen and Woodall numbers.
• Paul Leyland, Generalized Cullen and Woodall numbers.
• Index entries for linear recurrences with constant coefficients, signature (11,-35,25).

Crossrefs

Cf. A003261, A036291.

Programs

Magma

[n*5^n - 1: n in [1..30]]; // Vincenzo Librandi, Jun 21 2018

Mathematica

Table[n*5^n-1,{n,20}] (* or *) LinearRecurrence[{11,-35,25},{4,49,374},20] (* Harvey P. Dale, Jun 25 2017 *)
CoefficientList[Series[(4 + 5 x - 25 x^2) / ((1 - 5 x)^2 (1 - x)), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 21 2018 *)

PARI

a(n) = { n*5^n - 1 } \\ Harry J. Smith, Sep 24 2009

Formula

G.f.: x*(4 + 5*x - 25*x^2)/((1 - 5*x)^2*(1 - x)). - Vincenzo Librandi, Jun 21 2018

a(n) = A036291(n) - 1. - Michel Marcus, Jun 21 2018

From Elmo R. Oliveira, May 05 2025: (Start)

E.g.f.: 1 + exp(x)*(5*x*exp(4*x) - 1).

a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3) for n > 3. (End)