A351788 a(1) = 1; a(n) = a(n-1) + Sum_{d|n, 1 < d < n} a(n/d) * a(d).

1, 1, 1, 2, 2, 4, 4, 8, 9, 13, 13, 25, 25, 33, 37, 57, 57, 83, 83, 117, 125, 151, 151, 233, 237, 287, 305, 387, 387, 503, 503, 649, 675, 789, 805, 1073, 1073, 1239, 1289, 1607, 1607, 1955, 1955, 2309, 2419, 2721, 2721, 3465, 3481, 4007, 4121, 4795, 4795, 5643, 5695

Offset

1,4

Links

Table of n, a(n) for n=1..55.

Formula

G.f.: ( x + Sum_{i>=2} Sum_{j>=2} a(i) * a(j) * x^(i*j) ) / (1 - x).

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[If[1 < d < n, a[n/d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 55}]

Crossrefs

Cf. A038044, A084978, A122698, A277120, A339755, A341697, A345139, A351787.

Sequence in context: A222955 A217208 A287136 * A183565 A222708 A324843

Adjacent sequences: A351785 A351786 A351787 * A351789 A351790 A351791

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2022

Status

approved