A064758 a(n) = n*12^n - 1.

11, 287, 5183, 82943, 1244159, 17915903, 250822655, 3439853567, 46438023167, 619173642239, 8173092077567, 106993205379071, 1390911669927935, 17974858503684095, 231105323618795519, 2958148142320582655, 37716388814587428863, 479219999055934390271, 6070119988041835610111, 76675199848949502443519

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 (25,-168,144).

Crossrefs

Cf. for a(n) = n*k^n - 1: -A000012(k=0), A001477(k=1), A003261 (k=2), A060352 (k=3), A060416 (k=4), A064751 (k=5), A064752 (k=6), A064753 (k=7), A064754 (k=8), A064755 (k=9), A064756 (k=10), A064757 (k=11), this sequence (k=12).

Cf. A064750.

Programs

Magma

[n*12^n - 1: n in [1..30]]; // Vincenzo Librandi, Jun 21 2018

Mathematica

CoefficientList[Series[(11 + 12 x - 144 x^2) / ((1 - 12 x)^2 (1 - x)), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 21 2018 *)

PARI

a(n) = { n*12^n - 1 } \\ Harry J. Smith, Sep 24 2009

Formula

G.f.: x*(11 + 12*x - 144*x^2)/((1 - 12*x)^2*(1 - x)). - Vincenzo Librandi, Jun 21 2018

From Elmo R. Oliveira, Sep 07 2024: (Start)

E.g.f.: 1 + exp(x)*(12*x*exp(11*x) - 1).

a(n) = 25*a(n-1) - 168*a(n-2) + 144*a(n-3) for n > 3.

a(n) = A064750(n) - 2. (End)