A322752 Number of "funny trees" on n nodes.

0, 2, 3, 9, 30, 110, 423, 1706, 7085, 30186, 131071, 578194, 2583377, 11667874, 53180604, 244301512, 1129947243, 5257592237, 24592945975, 115578827200, 545478791124, 2584216074295, 12285025045259, 58584860422121, 280181867792399, 1343499543045511, 6457845289959966

Offset: 0

Author

N. J. A. Sloane, Dec 25 2018

Keywords

• nonn

Comments

For precise definition see Example 15.3.7 of Bona (2015).

The trees considered here have nodes of two types: black and white. The child nodes of black nodes are unordered and can be either black or white. The child nodes of white nodes are linearly ordered and must be black. - Andrew Howroyd, Feb 06 2025

References

• Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 1002.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• N. J. A. Sloane, Annotated scan of page 1001 of Bona (2015).
• N. J. A. Sloane, Annotated scan of page 1002 of Bona (2015).

Crossrefs

Cf. A277996.

Programs

PARI

EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
seq(n)={my(w=O(x),b=O(x)); for(n=1, n, w=x/(1-b); b=x*(1 + x*Ser(EulerT(Vec(b+w))))); Vec(b+w, -n-1)} \\ Andrew Howroyd, Feb 06 2025

Extensions

Offset corrected and a(7) onwards from Andrew Howroyd, Feb 06 2025