A386399 Number of forests with at most n unlabeled nodes.

1, 2, 4, 7, 13, 23, 43, 80, 156, 309, 638, 1348, 2949, 6607, 15206, 35720, 85625, 208588, 515787, 1291316, 3269194, 8355832, 21539988, 55942920, 146271594, 384746580, 1017522228, 2704227858, 7219183490, 19351410860, 52068524665, 140588391713, 380824067016

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Max A. Alekseyev, Allan Bickle, and Lucia Mazza, Forbidden Subgraphs of Single Trees, 2026. See p. 4 (Prop. 7).

Formula

G.f.: exp(sum_{k>0} B(x^k)/k ) / (1-x), where B(x) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 6*x^6 + 11*x^7 + ... = C(x)-1 and C is the g.f. for A000055.

Crossrefs

Partial sums of A005195.

Cf. A000272, A002807, A006897, A054548, A137917, A367863, A372176.

Sequence in context: A036256 A093629 A174566 * A018182 A005595 A296689

Adjacent sequences: A386396 A386397 A386398 * A386400 A386401 A386402

Keyword

nonn,easy

Author

Max Alekseyev, Jul 20 2025

Status

approved