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A030266 Shifts left under COMPOSE transform with itself. +0
24
0, 1, 1, 2, 6, 23, 104, 531, 2982, 18109, 117545, 808764, 5862253, 44553224, 353713232, 2924697019, 25124481690, 223768976093, 2062614190733, 19646231085928, 193102738376890, 1956191484175505, 20401540100814142 (list; graph; listen)
OFFSET

0,4

REFERENCES

David Callan, A Combinatorial Interpretation of the Eigensequence for Composition, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.4.

LINKS

N. J. A. Sloane, Transforms

FORMULA

G.f. A(x) satisfies the functional equation: A(x)-x = x*A(A(x)). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 04 2002

G.f.: A(x/(1+A(x))) = x. - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 04 2003

Suppose functions A=A(x), B=B(x), C=C(x), etc., satisfy: A = 1 + xAB, B = 1 + xABC, C = 1 + xABCD, D = 1 + xABCDE, etc., then B(x)=A(x*A(x)), C(x)=B(x*A(x)), D(x)=C(x*A(x)), etc., where A(x) = 1 + x*A(x)*A(x*A(x)) and x*A(x) is the g.f. of this sequence (see table A128325). - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 10 2007

G.f. A(x) = x*F(x,1) where F(x,n) satisfies: F(x,n) = F(x,n-1)*(1 + x*F(x,n+1)) for n>0 with F(x,0)=1. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2007

PROGRAM

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+x*A*subst(A, x, x*A+x*O(x^n))); polcoeff(A, n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 10 2007

CROSSREFS

Cf. A001028, A035049.

Cf. A110447.

Cf. A128325.

Sequence in context: A117106 A137534 A137535 this_sequence A110447 A137536 A137537

Adjacent sequences: A030263 A030264 A030265 this_sequence A030267 A030268 A030269

KEYWORD

nonn,nice,eigen

AUTHOR

Christian G. Bower (bowerc(AT)usa.net)

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.


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