A308023 G.f. A(x) satisfies: A(x) = x * (1 + (1/(1 - x)) * (A(x/(1 - x)) + A(x^2/(1 - x)^2) + A(x^3/(1 - x)^3) + ...)).

1, 1, 4, 14, 52, 208, 908, 4304, 22016, 120796, 706896, 4389752, 28800668, 198884648, 1440809932, 10918549748, 86331306980, 710609746752, 6076740094448, 53887906573064, 494734785732236, 4695242718593096, 45998992617959932, 464614423225361404, 4832633949407618644

Offset

1,3

Links

Table of n, a(n) for n=1..25.

Formula

a(1) = 1; a(n+1) = Sum_{k=1..n} binomial(n,k) * Sum_{d|k} a(d).

Mathematica

terms = 25; A[_] = 0; Do[A[x_] = x (1 + 1/(1 - x) Sum[A[x^k/(1 - x)^k], {k, 1, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
a[n_] := a[n] = Sum[Binomial[n - 1, k] Sum[a[d], {d, Divisors[k]}], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 25}]

Crossrefs

Cf. A003238, A040027, A308024.

Sequence in context: A370891 A284765 A129997 * A149489 A125783 A090319

Adjacent sequences: A308020 A308021 A308022 * A308024 A308025 A308026

Keyword

nonn

Author

Ilya Gutkovskiy, May 09 2019

Status

approved