A166725 a(n) = (2*n+1)*25^n.

1, 75, 3125, 109375, 3515625, 107421875, 3173828125, 91552734375, 2593994140625, 72479248046875, 2002716064453125, 54836273193359375, 1490116119384765625, 40233135223388671875, 1080334186553955078125, 28870999813079833984375, 768341124057769775390625

Offset: 0

Author

Jaume Oliver Lafont, Oct 20 2009

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (50,-625).

Crossrefs

Cf. A058962 ((2n+1)*4^n), A155988 ((2n+1)*9^n), A016578 (log(3/2)).

Programs

Magma

[(2*n+1)*25^n: n in [0..20]]; // Vincenzo Librandi, Jun 08 2011

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 *)

PARI

a(n)=(2*n+1)*25^n

Formula

G.f.: (1+25*x)/(1-25*x)^2.

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

E.g.f.: (50*x + 1)*exp(25*x). - G. C. Greubel, May 24 2016

Sum_{n>=0} (-1)^n/a(n) = 5*arctan(1/5). - Amiram Eldar, Feb 26 2022