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%I #16 Dec 26 2023 05:30:04
%S 1,2,5,11,25,51,110,221,456,918,1864,3729,7528,15057,30227,60485,
%T 121205,242411,485337,970675,1942307,3884730,7771327,15542655,
%U 31089330,62178686,124364903,248730268,497475717,994951435,1989934099,3979868199
%N Number of ways to represent n as a+b*(c+d*(e+f*(...x+y*(z)...))) in positive integers.
%H Robert Israel, <a href="/A084978/b084978.txt">Table of n, a(n) for n = 1..3305</a>
%F a(n+1) = Sum(k=1..n; Sum(d|k; a(d)).
%F a(n+1) = 1 + Sum(k=1..n; Sum(d|k; a(d)) or a(n+1) = a(n) + Sum(d|n; a(d)). - _Vladeta Jovovic_, Aug 08 2004
%F G.f. A(x) satisfies: A(x) = (x/(1 - x)) * (1 + Sum_{k>=1} A(x^k)). - _Ilya Gutkovskiy_, Feb 25 2020
%F a(n) ~ c * 2^n, where c = 0.9266495520163897954172886595779644507444342903568129920731434938761... - _Vaclav Kotesovec_, Dec 26 2023
%e a(3) = 5: 3 = 2+1(1) = 1+2(1) = 1+1(2) = 1+1(1+1(1)).
%p f:= proc(n) option remember; local d;
%p procname(n-1) + add(procname(d), d = numtheory:-divisors(n-1))
%p end proc:
%p f(1):=1:
%p map(f, [$1..40]); # _Robert Israel_, Dec 25 2023
%K nonn
%O 1,2
%A _David W. Wilson_, Jun 16 2003
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