A140983 E.g.f. is reversion of (2(1+x)log(1+x)+x^2+2x)/( (2+x)^2(1+x) ).

1, 3, 17, 145, 1663, 24031, 419521, 8592417, 202069759, 5367258479, 158934860321, 5191969220945, 185490468312767, 7194912503747775, 301130097048242561, 13526711564792340289, 649121580063333263359, 33142745983169890692559

Offset: 1

Author

Brian Drake, Jul 28 2008

Keywords

• easy
• nonn

Comments

a(n) is the number of labeled incomplete ternary trees on n vertices in which each left or middle child has a larger label than its parent and each right child has a smaller label than its parent. For example, a(2)=3 because we have 2L1, 2M1 and 1R2. Here aLb means a is a left child of b, etc.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A007889.

Programs

Maple

N:= 8: exp(RootOf(2*_Z*exp(_Z)-x*exp(_Z)-2*x*exp(_Z)^2-x*exp(_Z)^3 -1 +exp(_Z)^2))-1: series(%, x, N+1): convert(%, polynom): seq( i!*coeff(%, x, i), i=1..N);