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A308370 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + A(x^k))^k. 4

%I

%S 1,1,3,8,20,47,118,280,681,1640,3963,9523,23004,55377,133477,321597,

%T 775054,1867304,4499934,10842847,26127768,62958232,151708512,

%U 365562567,880881465,2122617010,5114772619,12324827128,29698572295,71563264162,172442689864,415527172616

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

%F G.f. A(x) satisfies: A(x) = x * exp(-Sum_{k>=1} Sum_{d|k} d^2 * (-A(x^d))^(k/d) / k).

%t terms = 32; A[_] = 0; Do[A[x_] = x Product[(1 + A[x^k])^k, {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest

%Y Cf. A050383, A091865, A308369, A308371, A308372.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 22 2019

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)