A307780 a(1) = 1; a(n+1) = Sum_{d|n, n/d odd} a(d)^(n/d).

1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 8, 9, 17, 18, 19, 29, 29, 30, 58, 59, 91, 157, 158, 159, 284, 317, 318, 445, 573, 574, 1161, 1162, 1162, 1676, 1677, 2830, 4071, 4072, 4073, 8988, 12113, 12114, 20134, 20135, 22183, 32681, 32682, 32683, 57072, 73457, 90265, 114656, 122848, 122849, 169533

Offset

1,4

Links

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

Formula

L.g.f.: log(Product_{n>=1} ((1 + a(n)*x^n)/(1 - a(n)*x^n))^(1/(2*n))) = Sum_{n>=1} a(n+1)*x^n/n.

Mathematica

a[n_] := a[n] = Sum[Boole[OddQ[(n - 1)/d]] a[d]^((n - 1)/d), {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 55}]

Crossrefs

Cf. A127525, A307781.

Sequence in context: A307779 A165684 A342519 * A340276 A340275 A348323

Adjacent sequences: A307777 A307778 A307779 * A307781 A307782 A307783

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 28 2019

Status

approved