OFFSET
0,3
COMMENTS
a(n) is also the number of {du,h}-avoiding generalized noncrossing trees.
The expression i/(2*j+i) *binomial(2*j+i,j) =A009766(i+j-1,j), is to be interpreted as 1 if i=j=0.
REFERENCES
Y. Sun, Z. Wang, String pattern avoidance in generalized non-crossing trees, Disc. Math. Theor. Comp. Sci. 11 (1) (2009) 79-94, proposition 3.4
MAPLE
A153233aux := proc(i, j)
if i=0 and j = 0 then
1;
else
i/(2*j+i)*binomial(2*j+i, j) ;
end if;
end proc:
A153233 := proc(n)
a := 0 ;
for i from 0 to n do
for j from 0 to n-i do
k := n-i-j ;
if k >= 0 then
a := a+ (-1)^k *binomial(3*i+2*j+k, k) *2^(i+j) *A000108(i) *A153233aux(i, j) ;
end if:
end do:
end do:
a ;
end proc: # R. J. Mathar, Dec 17 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Yidong Sun (sydmath(AT)yahoo.com.cn), Dec 21 2008
STATUS
approved