A308379 E.g.f. A(x) satisfies: A(x) = x * Product_{k>=1} 1/(1 - A(x^k))^(1/k).

1, 2, 15, 152, 2255, 40944, 938161, 25026896, 777966129, 27346727600, 1077001807871, 46870231698168, 2235954785893231, 115950345421719704, 6496012991027031585, 390935629387700612384, 25153144712405994085409, 1722934940168892344912928, 125180348349211811174365615

Offset: 1

Author

Ilya Gutkovskiy, May 23 2019

Keywords

• nonn

Crossrefs

Cf. A050383, A308369, A308380.

Programs

Mathematica

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

Formula

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