A339755 a(1) = 1; a(n+1) = 1 + Sum_{d|n} a(n/d) * a(d).
1, 2, 5, 11, 27, 55, 131, 263, 571, 1168, 2445, 4891, 10113, 20227, 40979, 82229, 165632, 331265, 665365, 1330731, 2666729, 5334769, 10679319, 21358639, 42740683, 85482096, 171004645, 342015001, 684113793, 1368227587, 2736633741, 5473267483, 10946869669, 21893763789, 43788190107
Offset: 1
Keywords
Programs
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Maple
a:= proc(n) option remember; uses numtheory; 1+add(a(d)*a((n-1)/d), d=divisors(n-1)) end: seq(a(n), n=1..35); # Alois P. Heinz, Dec 15 2020 -
Mathematica
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}]
Formula
G.f.: x * (1/(1 - x) + Sum_{i>=1} Sum_{j>=1} a(i) * a(j) * x^(i*j)).
a(n) ~ c * 2^n, where c = 1.27442410710035207761153205319824525254716841098942446508584158048310907298... - Vaclav Kotesovec, Dec 16 2020