OFFSET
1,1
COMMENTS
It appears that the limit a(n+1)/a(n) exists and is near 4.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..300
EXAMPLE
1 = 1/2 + 2^2/3^2 + 2^6/11^3 + 2^12/28^4 + 2^20/67^5 + 2^30/181^6 + 2^42/540^7 + 2^56/1605^8 + 2^72/4500^9 + 2^90/12770^10 + 2^110/37773^11 + 2^132/127030^12 + 2^156/444950^13 + 2^182/1379830^14 + 2^210/4396237^15 + 2^240/13632772^16 + 2^272/45274296^17 + 2^306/158468043^18 + 2^342/530856473^19 + 2^380/1800446217^20 + 2^420/6279909810^21 + ... + ( 2^(n-1)/a(n) )^n + ...
Incidentally,
Sum_{n>=1} 2^(n-1)/a(n) = 2.594806011516631787617662898514062588686879234...
Sum_{n>=1} 2^(n^2)/a(n)^n = 3.295922872490926100815120594347157182861242917...
Sum_{n>=1} 2^(n*(n+1))/a(n)^n = 14.82031378016256272989741456078817533736...
Sum_{n>=1} 1/a(n) = 0.983220030675069959469784597542593767565029822764...
PROG
(PARI) /* Must have appropriate precision for N terms: */ N = 100;
{A=[2]; for(i=1, N, A=concat(A, 1 + floor((1/(1 - sum(n=1, #A, (2^n)^(n-1)/A[n]^n *1.))*2^((#A)*(#A+1)) )^(1/(#A+1))) ) ; print1(#A, ", ")); A}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 27 2018
STATUS
approved