login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A171220 a(n) = (2n + 1)*5^n. 1
1, 15, 125, 875, 5625, 34375, 203125, 1171875, 6640625, 37109375, 205078125, 1123046875, 6103515625, 32958984375, 177001953125, 946044921875, 5035400390625, 26702880859375, 141143798828125, 743865966796875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Inserting x=1/sqrt(b) into the power series expansion of arctanh(x) yields the general BBP-type formula log((sqrt(b)+1)/(sqrt(b)-1))*sqrt(b)/2 = Sum_{k>=0} 1/((2k+1)b^k).

This sequence illustrates case b=5, with

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

David H. Bailey, Compendium of BBP formulas for mathematical constants (formula 53)

Index entries for linear recurrences with constant coefficients, signature (10,-25)

FORMULA

a(n) = 10*a(n-1) - 25*a(n-2).

O.g.f: (1+5*x)/(1-5*x)^2.

PROG

(PARI) a(n)=(2*n+1)*5^n

(MAGMA) [(2*n+1)*5^n: n in [0..25]]; // Vincenzo Librandi, Jun 08 2011

CROSSREFS

Cf. (2n+1)2^n A014480, (2n+1)*3^n A124647, (2n+1)*4^n A058962, (2n+1)9^n A155988, (2n+1)16^n A165283, (2n+1)25^n A166725.

Sequence in context: A264046 A027839 A034271 * A071080 A193365 A069975

Adjacent sequences:  A171217 A171218 A171219 * A171221 A171222 A171223

KEYWORD

nonn,easy

AUTHOR

Jaume Oliver Lafont, Dec 05 2009

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 December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)