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A308380 E.g.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + A(x^k))^(1/k). 1
1, 2, 9, 56, 455, 4224, 48391, 609104, 8814753, 140512400, 2483071481, 47387543928, 989622741367, 22107721563368, 530909919285495, 13581037512256544, 369627228319635329, 10633498287935101920, 323389433072136213289, 10342303284390333962600, 347514522157550224614711 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

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

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

CROSSREFS

Cf. A091865, A308370, A308379.

Sequence in context: A052860 A318289 A052840 * A036243 A179505 A211205

Adjacent sequences:  A308377 A308378 A308379 * A308381 A308382 A308383

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 23 2019

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)