A036292 a(n) = n*6^n.

0, 6, 72, 648, 5184, 38880, 279936, 1959552, 13436928, 90699264, 604661760, 3990767616, 26121388032, 169789022208, 1097098297344, 7052774768640, 45137758519296, 287753210560512, 1828079220031488, 11577835060199424, 73123168801259520, 460675963447934976

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-36).

Crossrefs

Cf. A000400.

Programs

Magma

[n*6^n: n in [0..30]]; // Vincenzo Librandi, Apr 10 2016

Maple

A036292:=n->n*6^n; seq(A036292(n), n=0..50); # Wesley Ivan Hurt, Nov 09 2013

Mathematica

Table[n*6^n, {n,0,50}] (* Wesley Ivan Hurt, Nov 08 2013 *)
LinearRecurrence[{12, -36}, {0, 6}, 25] (* Vincenzo Librandi, Apr 10 2016 *)

PARI

a(n) = n*6^n; \\ Michel Marcus, Nov 09 2013

Formula

a(n) = n*A000400(n). - Michel Marcus, Nov 09 2013

From Vincenzo Librandi, Apr 10 2016: (Start)

G.f.: 6*x/(1-6*x)^2.

a(n) = 12*a(n-1) - 36*a(n-2) for n > 1. (End)

From Amiram Eldar, Jul 20 2020: (Start)

Sum_{n>=1} 1/a(n) = log(6/5).

Sum_{n>=1} (-1)^(n+1)/a(n) = log(7/6). (End)

E.g.f.: 6*x*exp(6*x). - Elmo R. Oliveira, Sep 09 2024