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A351787
a(1) = 1; a(n+1) = a(n) + Sum_{d|n} a(n/d) * a(d).
2
1, 2, 6, 18, 58, 174, 546, 1638, 4986, 14994, 45214, 135642, 407838, 1223514, 3672726, 11018874, 33063498, 99190494, 297593514, 892780542, 2678403690, 8035217622, 24105833722, 72317501166, 216953071986, 650859219322, 1952579289318, 5857737927786, 17573218697070
OFFSET
1,2
FORMULA
G.f.: x * ( 1 + Sum_{i>=1} Sum_{j>=1} a(i) * a(j) * x^(i*j) ) / (1 - x).
MATHEMATICA
a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[a[(n - 1)/d] a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 29}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 19 2022
STATUS
approved