A351787 -id:A351787 - cp's OEIS frontend

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

Ilya Gutkovskiy, Feb 19 2022

nonn

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

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}]

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

A351797 a(1) = 1; a(n+1) = -a(n) + 2 * Sum_{d|n} a(n/d) * a(d).

Original entry on oeis.org

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

Ilya Gutkovskiy, Feb 19 2022

nonn

Cf. A038044, A084978, A122698, A277120, A339755, A341697, A345139, A351787, A351788.

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}]

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.

cp's OEIS Frontend

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

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