|
Search: id:A154920
|
|
|
| A154920 |
|
Denominators of a ternary BBP-type formula for ln(3) |
|
+0
8
|
|
| 1, 18, 27, 324, 405, 4374, 5103, 52488, 59049, 590490, 649539, 6377292, 6908733, 66961566, 71744535, 688747536, 731794257, 6973568802, 7360989291, 69735688020, 73222472421, 690383311398, 721764371007, 6778308875544
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
ln(3) = sum(k>=0, {9/(2k+1)+1/(2k+2)}/9^(k+1) )
ln(3) = 1 + sum(k>=0, {1/(2k+2)+1/(2k+3)}/9^(k+1) )
|
|
LINKS
|
David H. Bailey, A Compendium of BBP-Type Formulas for Mathematical Constants, page 14. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 25 2009]
|
|
FORMULA
|
a(n)=(n+1)*9^[(n+1)/2]=18*a(n-2)-81*a(n-4)
sum(n>=0,1/a(n))=ln(3)
G.f.: (1+18*x+9*x^2)/(1-9*x^2)^2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Jan 29 2009]
a(n)=(2-(-1)^n)*(n+1)*3^n [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 27 2009]
|
|
PROGRAM
|
(PARI) a(n)=(n+1)*9^((n+1)\2) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 25 2009]
|
|
CROSSREFS
|
Cf. A002391,A058962.
Cf. A164985, A165132. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 25 2009]
Sequence in context: A038632 A138336 A166630 this_sequence A094224 A128858 A141782
Adjacent sequences: A154917 A154918 A154919 this_sequence A154921 A154922 A154923
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Jan 17 2009, Jan 18 2009
|
|
|
Search completed in 0.002 seconds
|
