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

1, 1, 3, 8, 20, 47, 118, 280, 681, 1640, 3963, 9523, 23004, 55377, 133477, 321597, 775054, 1867304, 4499934, 10842847, 26127768, 62958232, 151708512, 365562567, 880881465, 2122617010, 5114772619, 12324827128, 29698572295, 71563264162, 172442689864, 415527172616

Offset: 1

Author

Ilya Gutkovskiy, May 22 2019

Keywords

• nonn

Crossrefs

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

Programs

Mathematica

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

Formula

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