|
|
A166725
|
|
a(n) = (2*n+1)*25^n.
|
|
2
|
|
|
1, 75, 3125, 109375, 3515625, 107421875, 3173828125, 91552734375, 2593994140625, 72479248046875, 2002716064453125, 54836273193359375, 1490116119384765625, 40233135223388671875, 1080334186553955078125, 28870999813079833984375, 768341124057769775390625
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1+25*x)/(1-25*x)^2.
Sum_{k>=0} 1/a(k) = (5/2)*log(3/2).
Sum_{n>=0} (-1)^n/a(n) = 5*arctan(1/5). - Amiram Eldar, Feb 26 2022
|
|
MATHEMATICA
|
Table[5^(2*n) *(2*n + 1), {n, 0, 10}] (* G. C. Greubel, May 24 2016 *)
LinearRecurrence[{50, -625}, {1, 75}, 30] (* Harvey P. Dale, Mar 02 2018 *)
|
|
PROG
|
(PARI) a(n)=(2*n+1)*25^n
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|