A308379 - OEIS

%I #7 May 24 2019 13:07:36

%S 1,2,15,152,2255,40944,938161,25026896,777966129,27346727600,

%T 1077001807871,46870231698168,2235954785893231,115950345421719704,

%U 6496012991027031585,390935629387700612384,25153144712405994085409,1722934940168892344912928,125180348349211811174365615

%N E.g.f. A(x) satisfies: A(x) = x * Product_{k>=1} 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 = 19; A[_] = 0; Do[A[x_] = x Product[1/(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. A050383, A308369, A308380.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, May 23 2019