A064753 a(n) = n*7^n - 1.

6, 97, 1028, 9603, 84034, 705893, 5764800, 46118407, 363182462, 2824752489, 21750594172, 166095446411, 1259557135290, 9495123019885, 71213422649144, 531726889113615, 3954718737782518, 29311444762388081, 216579008522089716, 1595845325952240019, 11729463145748964146

Offset: 1

Author

N. J. A. Sloane, Oct 19 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Paul Leyland, Factors of Cullen and Woodall numbers.
• Paul Leyland, Generalized Cullen and Woodall numbers.
• Index entries for linear recurrences with constant coefficients, signature (15,-63,49).

Crossrefs

For a(n)=n*k^n-1 cf. -A000012 (k=0), A001477 (k=1), A003261 (k=2), A060352 (k=3), A060416 (k=4), A064751 (k=5), A064752 (k=6), this sequence (k=7), A064754 (k=8), A064755 (k=9), A064756 (k=10), A064757 (k=11), A064758 (k=12).

Cf. A036293.

Programs

Magma

[ n*7^n-1: n in [1..20]]; // Vincenzo Librandi, Sep 16 2011

Maple

k:= 7; f:= gfun:-rectoproc({1 + (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(1) = k-1}, a(n), remember): map(f, [$1..20]); # Georg Fischer, Feb 19 2021

Mathematica

Table[n 7^n-1,{n,20}] (* or *) LinearRecurrence[{15,-63,49},{6,97,1028},20] (* Harvey P. Dale, Feb 12 2022 *)

Formula

From Alois P. Heinz, Feb 19 2021: (Start)

G.f.: (56*x^2-21*x+1)/((x-1)*(7*x-1)^2).

a(n) = A036293(n) - 1. (End)

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

E.g.f.: 1 + exp(x)*(7*x*exp(6*x) - 1).

a(n) = 15*a(n-1) - 63*a(n-2) + 49*a(n-3) for n > 3. (End)