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Search: id:A119013
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| A119013 |
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Eigenvector of triangle A118588; E.g.f. satisfies: A(x) = exp(x)*A(x^2+x^3). |
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3
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| 1, 1, 3, 13, 73, 621, 5491, 60313, 743793, 10115353, 158914531, 2815311621, 55094081593, 1142894689093, 25142695616403, 594557634923281, 15084112106943841, 407999468524242993, 11669035487641120963
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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)). ]
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FORMULA
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Log(A(x)) = o.g.f. of A014535 (B-trees of order 3 with n leaves).
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EXAMPLE
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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 +...
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PROGRAM
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(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)))}
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CROSSREFS
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Cf. A118588 (triangle), A118589 (row sums), A014535 (log(A(x)).
Sequence in context: A124468 A128196 A162161 this_sequence A156154 A020094 A009382
Adjacent sequences: A119010 A119011 A119012 this_sequence A119014 A119015 A119016
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 08 2006
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