|
%I #10 Feb 06 2022 16:41:13
%S 1,3,17,145,1663,24031,419521,8592417,202069759,5367258479,
%T 158934860321,5191969220945,185490468312767,7194912503747775,
%U 301130097048242561,13526711564792340289,649121580063333263359,33142745983169890692559
%N E.g.f. is reversion of (2(1+x)log(1+x)+x^2+2x)/( (2+x)^2(1+x) ).
%C 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.
%H Alois P. Heinz, <a href="/A140983/b140983.txt">Table of n, a(n) for n = 1..100</a>
%p 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);
%Y Cf. A007889.
%K easy,nonn
%O 1,2
%A _Brian Drake_, Jul 28 2008
|
