A308371 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} 1/(1 - k*A(x^k)).

1, 1, 4, 12, 42, 135, 500, 1797, 6885, 26612, 105561, 423734, 1726531, 7101261, 29486169, 123341520, 519422274, 2199966624, 9365714175, 40052639066, 171985425594, 741214499791, 3205096564624, 13901238793616, 60460193311425, 263627546862787, 1152207975128287

Offset: 1

Author

Ilya Gutkovskiy, May 22 2019

Keywords

• nonn

Crossrefs

Cf. A050383, A091865, A308369, A308370, A308372.

Programs

Mathematica

terms = 27; A[] = 0; Do[A[x] = x Product[1/(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).