OFFSET
0,3
COMMENTS
E.g.f. of triangle A118588 is exp(x + y*(x^2+x^3)); note the similarity to the e.g.f. of this sequence. More generally, the e.g.f. of an eigenvectors can be determined from the e.g.f. of a triangle as follows. [ Given a triangle with e.g.f.: exp(x + y*x*F(x)) such that F(0) = 0, then the eigenvector has e.g.f.: exp(G(x)) where o.g.f. G(x) satisfies: G(x) = x + G(x*F(x)). ]
FORMULA
Log(A(x)) = o.g.f. of A014535 (B-trees of order 3 with n leaves).
EXAMPLE
A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 73*x^4/4! + 621*x^5/5! +...
log(A(x)) = o.g.f. of A014535 =
x + x^2+ x^3+ x^4+ 2*x^5+ 2*x^6+ 3*x^7+ 4*x^8+ 5*x^9+ 8*x^10 +...
PROG
(PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, a(k)*n!*polcoeff(polcoeff(exp(x+y*(x^2+x^3)+x*O(x^n)+y*O(y^k)), n, x), k, y)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 08 2006
STATUS
approved