A090594 G.f. satisfies: A(x + x*A(-x)) = x + x*A(x).

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

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*x-C); polcoeff(A, n, x))}

Crossrefs

Cf. A006196.

Sequence in context: A363110 A271207 A091175 * A361912 A188496 A369079

Adjacent sequences: A090591 A090592 A090593 * A090595 A090596 A090597

Keyword

nonn

Author

Paul D. Hanna, Dec 05 2003

Status

approved