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%I #7 Dec 17 2012 10:42:20
%S 1,1,5,27,157,957,6025,38847,255161,1701297,11485549,78362091,
%T 539518389,3744085725,26164480017,183976884639,1300803253617,
%U 9242988233025,65971342007125,472779083030619,3400653965846093,24543058771387485,177678278627756185
%N a(n) = sum_{i+j+k=n} (-1)^k*binomial(3*i+2*j+k,k) * (i/(2*j+i)) * binomial(2*j+i,j) *2^(i+j) * Catalan(i).
%C a(n) is also the number of {du,h}-avoiding generalized noncrossing trees.
%C 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.
%D 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
%p A153233aux := proc(i,j)
%p if i=0 and j = 0 then
%p 1;
%p else
%p i/(2*j+i)*binomial(2*j+i,j) ;
%p end if;
%p end proc:
%p A153233 := proc(n)
%p a := 0 ;
%p for i from 0 to n do
%p for j from 0 to n-i do
%p k := n-i-j ;
%p if k >= 0 then
%p a := a+ (-1)^k *binomial(3*i+2*j+k,k) *2^(i+j) *A000108(i) *A153233aux(i,j) ;
%p end if:
%p end do:
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Dec 17 2012
%K nonn
%O 0,3
%A Yidong Sun (sydmath(AT)yahoo.com.cn), Dec 21 2008
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