A007860 Maximal matchings in rooted plane trees on n nodes.

1, 1, 4, 12, 44, 175, 718, 3052, 13308, 59139, 266974, 1220879, 5643562, 26327769, 123793450, 586078393, 2791408028, 13365916545, 64302770488, 310672722803, 1506737267266, 7332920012492, 35800278685252, 175286440178448, 860517328379634, 4234766396436095

Offset: 1

Author

Martin Klazar (klazar(AT)kam.mff.cuni.cz)

Keywords

• nonn

Links

• M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.
• Index entries for sequences related to rooted trees

Formula

G.f. f(x) satisfies f(x)^7 - (6+x) * f(x)^6 + (15+6*x) * f(x)^5 + (x^2-15*x-20) * f(x)^4 - (2*x^2-20*x-15) * f(x)^3 - (15*x+6) * f(x)^2 + (2*x^2+6*x+1) * f(x) + x^4 - x^2 - x = 0 [from Klazar]. - Sean A. Irvine, Feb 07 2018

Extensions

a(1) corrected and more terms from Sean A. Irvine, Feb 07 2018