OFFSET
0,1
COMMENTS
This constant plus A292179 equals log(2), due to the identity (at x = 1/2):
Sum_{n=-oo..+oo, n<>0} (x - x^n)^n / n = -log(1-x).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..500
FORMULA
Constant: Sum_{n>=1} -(-1)^n * 2^n / (n * (2^(n+1) - 1)^n).
Constant: log(2) - Sum_{n>=1} (2^(n-1) - 1)^n / (n * 2^(n^2)).
EXAMPLE
Constant t = 0.62663613878943633971922411728096265924408333843433690026313290...
where t = 2/(1*3) - 4/(2*7^2) + 8/(3*15^3) - 16/(4*31^4) + 32/(5*63^5) - 64/(6*127^6) + 128/(7*255^7) - 256/(8*511^8) + 512/(9*1023^9) - 1024/(10*2047^10) + 2048/(11*4095^11) - 4096/(12*8191^12) + 8192/(13*16383^13) - 16384/(14*32767^14) + 32768/(15*65535^15) +...
Also,
log(2) - t = 0/(1*2) + 1^2/(2*2^4) + 3^3/(3*2^9) + 7^4/(4*2^16) + 15^5/(5*2^25) + 31^6/(6*2^36) + 63^7/(7*2^49) + 127^8/(8*2^64) + 255^9/(9*2^81) + 511^10/(10*2^100) + 1023^11/(11*2^121) + 2047^12/(12*2^144) + 4095^13/(13*2^169) + 8191^14/(14*2^196) + 16383^15/(15*2^225) +... (constant A292179)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paul D. Hanna, Oct 05 2017
STATUS
approved