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A351797
a(1) = 1; a(n+1) = -a(n) + 2 * Sum_{d|n} a(n/d) * a(d).
0
1, 1, 3, 9, 29, 87, 273, 819, 2493, 7497, 22607, 67821, 203919, 611757, 1836363, 5509437, 16531749, 49595247, 148796757, 446390271, 1339201845, 4017608811, 12052916861, 36158750583, 108476535993, 325429609661, 976289644659, 2928868963893, 8786609348535
OFFSET
1,3
FORMULA
G.f.: x * ( 1 + 2 * Sum_{i>=1} Sum_{j>=2} a(i) * a(j) * x^(i*j) ) / (1 - x).
a(n) = A351787(n) / 2 for n > 1.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = -a[n - 1] + 2 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