login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A116165 a(n) = 7^n * n*(n+1). 1
0, 14, 294, 4116, 48020, 504210, 4941258, 46118408, 415065672, 3631824630, 31072277390, 261007130076, 2159240803356, 17633799894074, 142426845298290, 1139414762386320, 9039357114931472, 71184937280085342, 556917450485373558 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (21,-147,343).

FORMULA

G.f.: 14*x/(1-7*x)^3. - Vincenzo Librandi, Feb 28 2013

a(n) = 21*a(n-1) - 147*a(n-2) + 343*a(n-3). - Vincenzo Librandi, Feb 28 2013

a(n+1) = 14*A027474(n+2). - Bruno Berselli, Feb 28 2013

E.g.f.: 7*x*(2 + 7*x)*exp(7*x). - G. C. Greubel, May 11 2019

From Amiram Eldar, Jul 20 2020: (Start)

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

Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(8/7) - 1. (End)

MATHEMATICA

Table[(n^2 + n) 7^n, {n, 0, 30}] (* Vincenzo Librandi, Feb 28 2013 *)

PROG

(MAGMA) [(n^2+n)*7^n: n in [0..30]]; /* or */ I:=[0, 14, 294]; [n le 3 select I[n] else 21*Self(n-1)-147*Self(n-2)+343*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 28 2013

(PARI) a(n)=(n^2+n)*7^n \\ Charles R Greathouse IV, Feb 28 2013

(Sage) [7^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 11 2019

(GAP) List([0..30], n-> 7^n*n*(n+1)) # G. C. Greubel, May 11 2019

CROSSREFS

Cf. A007758, A036289, A027474, A128796.

Sequence in context: A215869 A262740 A158475 * A186376 A034834 A276699

Adjacent sequences:  A116162 A116163 A116164 * A116166 A116167 A116168

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian, Apr 08 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)