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A153233 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). 1
1, 1, 5, 27, 157, 957, 6025, 38847, 255161, 1701297, 11485549, 78362091, 539518389, 3744085725, 26164480017, 183976884639, 1300803253617, 9242988233025, 65971342007125, 472779083030619, 3400653965846093, 24543058771387485, 177678278627756185 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=0..22.

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

Sequence in context: A098409 A052227 A101386 * A084076 A337011 A081924

Adjacent sequences:  A153230 A153231 A153232 * A153234 A153235 A153236

KEYWORD

nonn

AUTHOR

Yidong Sun (sydmath(AT)yahoo.com.cn), Dec 21 2008

STATUS

approved

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Last modified September 23 16:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)