

A090594


G.f. satisfies: A(x + x*A(x)) = x + x*A(x).


1



0, 1, 2, 4, 10, 28, 92, 328, 1330, 5740, 27596, 139160, 769964, 4423736, 27567048, 177127440, 1223262698, 8667225836, 65523382052, 506370134232, 4150248267164, 34679055629960, 305773367599064, 2742997917079984, 25853946568986188
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OFFSET

0,3


COMMENTS

Series reversion of g.f. A(x) is A(x). The g.f. for A006196 (leftist trees with n leaves) also satisfies this condition: A(A(x)) = x. This sequence was inspired by communication with Michael Somos, while he was investigating this and similar functional equations and their resulting sequences.


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..270


FORMULA

G.f.: A(A(x)) = x.


PROG

(PARI) {a(n)=local(A); if(n<0, 0, A=x+x*O(x^n); for(i=1, n, B=subst(A, x, x); C=subst(A, x, x+x*B); A=A+x+A*xC); polcoeff(A, n, x))}


CROSSREFS

Cf. A006196.
Sequence in context: A229046 A271207 A091175 * A188496 A191501 A085549
Adjacent sequences: A090591 A090592 A090593 * A090595 A090596 A090597


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Dec 05 2003


STATUS

approved



