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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)