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

Author

Max Alekseyev, Jul 20 2025

Keywords

• nonn
• easy

Links

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

Crossrefs

Partial sums of A005195.

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

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.