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A120607 G.f. satisfies: 37*A(x) = 36 + 81*x + A(x)^10, starting with [1,3,15]. 19
1, 3, 15, 270, 5505, 124818, 3028200, 76896180, 2018211930, 54311811330, 1490518569747, 41556060361920, 1173726329836125, 33513124885393020, 965755118941566180, 28051840723006217040, 820439774630057541690 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

G.f.: A(x) = 1 + Series_Reversion((1+37*x - (1+x)^10)/81). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(9*n,n)/(8*n+1) * (36+81*x)^(8*n+1)/37^(9*n+1). - Paul D. Hanna, Jan 24 2008

EXAMPLE

A(x) = 1 + 3*x + 15*x^2 + 270*x^3 + 5505*x^4 + 124818*x^5 +...

A(x)^10 = 1 + 30*x + 555*x^2 + 9990*x^3 + 203685*x^4 + 4618266*x^5 +...

PROG

(PARI) {a(n)=local(A=1+3*x+15*x^2+x*O(x^n)); for(i=0, n, A=A+(-37*A+36+81*x+A^10)/27); polcoeff(A, n)}

CROSSREFS

Cf. A120588 - A120606.

Sequence in context: A050474 A051179 A122591 * A013352 A013354 A013356

Adjacent sequences:  A120604 A120605 A120606 * A120608 A120609 A120610

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 16 2006

STATUS

approved

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Last modified May 28 21:38 EDT 2017. Contains 287241 sequences.