OFFSET
1,1
LINKS
Maxie Dion Schmidt, A catalog of interesting and useful Lambert series identities, arXiv:2004.02976 [math.NT], 2020.
Eric Weisstein's World of Mathematics, Lambert Series.
Wikipedia, Lambert series.
FORMULA
Equals Sum_{k>=1} k^2/(2^k - 1).
Faster converging series: Sum_{n >= 1} (1/2)^(n^2)*( n^2*(8^n) - ((n-1)^2 - 2)*4^n - ((n+1)^2 - 2)*(2^n) + n^2 )/(2^n - 1)^3. - Peter Bala, Jan 19 2021
EXAMPLE
7.099285178890907114033125022164753663157608833211895...
MAPLE
evalf(add( (1/2)^(n^2)*( n^2*(8^n) - ((n-1)^2 - 2)*4^n - ((n+1)^2 - 2)*(2^n) + n^2 )/(2^n - 1)^3, n = 1..20 ), 100); # Peter Bala, Jan 22 2021
MATHEMATICA
RealDigits[Sum[n^2/(2^n - 1), {n, 1, 500}], 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 21 2020
STATUS
approved