0,4

J. A. Fill and R. P. Dobrow, The number of m-ary search trees on n keys, Combin. Probab. Comput. 6 (1997), 435-453.

Index entries for sequences related to rooted trees

a(0)=a(1)=1 and for n>=2 a(n)= sum( i+j+k=n-2, a(i)*a(j)*a(k) ) (i, j, k>=0) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 14 2004

G.f. A(x) satisfies A(x)= 1+ x+ x^2*A(x)^3 . - Michael Somos Mar 29 2007

Given g.f. A(x), then x*A(-x) is series reversion of A025262(n-1). - Michael Somos Mar 29 2007

A:= proc(n) option remember; if n=0 then 1 else convert (series (1+x+x^2*A(n-1)^3, x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n): seq (a(n), n=0..27); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]

(PARI) v=vector(50, j, 1); for(n=3, 50, A=sum(i=1, n, sum(j=1, n, sum(k=1, n, if(i+j+k-n, 0, v[i]*v[j]*v[k])))); v[n]=A); a(n)=v[n+1];

(PARI) {a(n)= local(A); if(n<0, 0, A= 1+O(x); forstep(k= 1, n, 2, A= 1+x+x*x*A^3); polcoeff(A, n))} /* Michael Somos Mar 29 2007 */

(PARI) {a(n)= if(n<0, 0, (-1)^n* polcoeff( serreverse((1-sqrt(1-4*x+4*x^3+x^2*O(x^n)))/2), n+1))} /* Michael Somos Mar 29 2007 */

Sequence in context: A096745 A027088 A027102 this_sequence A091488 A007561 A107269

Adjacent sequences: A019494 A019495 A019496 this_sequence A019498 A019499 A019500

nonn

James Fill (jimfill(AT)jhu.edu)

More terms 07/97 by Olivier Gerard (olivier.gerard(AT)gmail.com)