A307816 a(1) = 1; a(n) = Sum_{k=1..n-1} a(n-k) * Sum_{d|k} a(d)*a(k/d).

1, 1, 3, 11, 46, 201, 928, 4399, 21431, 106399, 536896, 2744532, 14185314, 73999955, 389131156, 2060478226, 10976863244, 58792036053, 316397505099, 1710037259744, 9277953713444, 50514377326158, 275903656802218, 1511334791637679, 8300811367229306, 45703063861360901

Offset: 1

Author

Ilya Gutkovskiy, Apr 30 2019

Keywords

• nonn

Crossrefs

Cf. A038044, A317875.

Programs

Mathematica

a[n_] := a[n] = Sum[a[n - k] Sum[a[d] a[k/d], {d, Divisors[k]}], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 26}]
a[n_] := a[n] = SeriesCoefficient[x + Sum[a[k] x^k, {k, 1, n - 1}]  Sum[Sum[a[i] a[j] x^(i j), {j, 1, n - 1}], {i, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 26}]

PARI

lista(nn) = { my(va=vector(nn)); va[1] = 1; for (n=2, nn, va[n] = sum(k=1, n-1, va[n-k] * sumdiv(k, d, va[d]*va[k/d]))); va;} \\ Michel Marcus, Apr 30 2019

Formula

G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x + (Sum_{n>=1} a(n)*x^n) * (Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)).