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A339755 a(1) = 1; a(n+1) = 1 + Sum_{d|n} a(n/d) * a(d).

%I A339755 #7 Dec 16 2020 08:05:58
%S A339755 1,2,5,11,27,55,131,263,571,1168,2445,4891,10113,20227,40979,82229,
%T A339755 165632,331265,665365,1330731,2666729,5334769,10679319,21358639,
%U A339755 42740683,85482096,171004645,342015001,684113793,1368227587,2736633741,5473267483,10946869669,21893763789,43788190107
%N A339755 a(1) = 1; a(n+1) = 1 + Sum_{d|n} a(n/d) * a(d).
%F A339755 G.f.: x * (1/(1 - x) + Sum_{i>=1} Sum_{j>=1} a(i) * a(j) * x^(i*j)).
%F A339755 a(n) ~ c * 2^n, where c = 1.27442410710035207761153205319824525254716841098942446508584158048310907298... - _Vaclav Kotesovec_, Dec 16 2020
%p A339755 a:= proc(n) option remember; uses numtheory;
%p A339755       1+add(a(d)*a((n-1)/d), d=divisors(n-1))
%p A339755     end:
%p A339755 seq(a(n), n=1..35);  # _Alois P. Heinz_, Dec 15 2020
%t A339755 a[1] = 1; a[n_] := a[n] = 1 + Sum[a[(n - 1)/d] a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 35}]
%Y A339755 Cf. A038044, A068336, A097558, A122698, A277120, A325303.
%K A339755 nonn
%O A339755 1,2
%A A339755 _Ilya Gutkovskiy_, Dec 15 2020