OFFSET
1,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..300
Frank Ellermann, Illustration of binomial transforms.
Index entries for linear recurrences with constant coefficients, signature (14,-49).
FORMULA
a(n) = n*7^(n-1).
a(n) = 14*a(n-1) - 49*a(n-2) with a(1) = 1, a(2) = 14.
a(n) = A003415(7^n). - Bruno Berselli, Oct 22 2013
From Amiram Eldar, Oct 28 2020: (Start)
Sum_{n>=1} 1/a(n) = 7*log(7/6).
Sum_{n>=1} (-1)^(n+1)/a(n) = 7*log(8/7). (End)
From Stefano Spezia, May 05 2024: (Start)
G.f.: x/(1 - 7*x)^2.
E.g.f.: x*exp(7*x). (End)
MATHEMATICA
Join[{a=1, b=14}, Table[c=14*b-49*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{14, -49}, {1, 14}, 19] (* Stefano Spezia, May 05 2024 *)
PROG
(Magma) [n*7^(n-1): n in [1..35]]; // Vincenzo Librandi, Jun 06 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001
Offset changed from 2 to 1 by Vincenzo Librandi, Jun 06 2011
STATUS
approved