A308372 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + k*A(x^k)).

1, 1, 3, 8, 19, 45, 110, 259, 614, 1466, 3479, 8239, 19581, 46445, 110209, 261555, 620649, 1472597, 3494663, 8292514, 19677729, 46694303, 110804310, 262932172, 623928374, 1480555791, 3513297447, 8336903884, 19783134767, 46944538382, 111397439864, 264341463510

Offset: 1

Author

Ilya Gutkovskiy, May 22 2019

Keywords

• nonn

Crossrefs

Cf. A050383, A091865, A308369, A308370, A308371.

Programs

Mathematica

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

Formula

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