A308380 E.g.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + A(x^k))^(1/k).

1, 2, 9, 56, 455, 4224, 48391, 609104, 8814753, 140512400, 2483071481, 47387543928, 989622741367, 22107721563368, 530909919285495, 13581037512256544, 369627228319635329, 10633498287935101920, 323389433072136213289, 10342303284390333962600, 347514522157550224614711

Offset: 1

Author

Ilya Gutkovskiy, May 23 2019

Keywords

• nonn

Crossrefs

Cf. A091865, A308370, A308379.

Programs

Mathematica

terms = 21; A[] = 0; Do[A[x] = x Product[(1 + A[x^k])^(1/k), {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] Range[0, terms]! // Rest

Formula

E.g.f. A(x) satisfies: A(x) = x * exp(-Sum_{k>=1} Sum_{d|k} (-A(x^d))^(k/d) / k).