A165283 a(n) = (2*n + 1)*16^n.

1, 48, 1280, 28672, 589824, 11534336, 218103808, 4026531840, 73014444032, 1305670057984, 23089744183296, 404620279021568, 7036874417766400, 121597189939003392, 2089670227099910144, 35740566642812256256, 608742554432415203328, 10330176681277348904960

Offset: 0

Author

Jaume Oliver Lafont, Sep 13 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (32,-256).

Crossrefs

Cf. A058962 ((2n+1)4^n), A155988 ((2n+1)9^n).

Programs

Magma

[(2*n+1)*16^n: n in [0..20]]; // Vincenzo Librandi, Jun 08 2011

PARI

a(n)=(2*n+1)*16^n

Formula

G.f.: (1+16*x)/(1-16*x)^2.

Sum_{n>=0} 1/a(n) = 2*log(5/3).

Sum_{n>=0} (-1)^n/a(n) = 4 * arctan(1/4). - Amiram Eldar, Jul 12 2020

E.g.f.: exp(16*x)*(1 + 32*x). - Stefano Spezia, May 09 2023