|
Search: id:A110626
|
|
|
| A110626 |
|
Denominator of b(n) = -Sum(k=1 to n, A037861(k)/((2k)(2k+1))), where A037861(k) = (number of 0's) - (number of 1's) in binary representation of k. |
|
+0
5
|
|
| 6, 6, 14, 504, 27720, 360360, 360360, 765765, 765765, 765765, 1601145, 1601145, 369495, 3061530, 94907430, 16703707680, 116925953760, 4326260289120, 1068586291412640, 43812037947918240, 1883917631760484320
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Denominators of partial sums of a series for log 4/Pi. Numerators are A110625.
|
|
REFERENCES
|
J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005) 61-65.
|
|
LINKS
|
J. Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi)
|
|
FORMULA
|
lim(n -> infinity, b(n)) = log 4/Pi = 0.24156...
|
|
EXAMPLE
|
a(3) = 14 because b(3) = 1/6 + 0 + 1/21 = 3/14.
|
|
CROSSREFS
|
Cf. A037861, A073099, A094640, A110625.
Sequence in context: A115014 A141378 A003871 this_sequence A072695 A085596 A107620
Adjacent sequences: A110623 A110624 A110625 this_sequence A110627 A110628 A110629
|
|
KEYWORD
|
easy,frac,nonn
|
|
AUTHOR
|
Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 01 2005
|
|
|
Search completed in 0.002 seconds
|
