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

%I

%S 1,2,9,56,455,4224,48391,609104,8814753,140512400,2483071481,

%T 47387543928,989622741367,22107721563368,530909919285495,

%U 13581037512256544,369627228319635329,10633498287935101920,323389433072136213289,10342303284390333962600,347514522157550224614711

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

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

%t 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

%Y Cf. A091865, A308370, A308379.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, May 23 2019

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)