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A322752
Number of "funny trees" on n nodes.
1
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
0,2
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.
PROG
(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
CROSSREFS
Cf. A277996.
Sequence in context: A275165 A073950 A281270 * A386925 A277345 A259943
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 25 2018
EXTENSIONS
Offset corrected and a(7) onwards from Andrew Howroyd, Feb 06 2025
STATUS
approved