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A159608 G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x*A(x)^3). 3
1, 1, 5, 46, 597, 9791, 191876, 4348394, 111561125, 3192096511, 100729014305, 3474750994936, 130094553648612, 5254546985647116, 227771218849108212, 10548385893161367506, 519835256567911242341, 27164324421130818956039 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

FORMULA

G.f. satisfies: A(x) = 1 + x*(2 - A(x))*A(x)^3 + 3*x^2*A'(x)*A(x)^2.

a(n) ~ c * 3^n * n! * n^(1/3), where c = 0.242604467523310747298... - Vaclav Kotesovec, Aug 24 2017

EXAMPLE

G.f.: A(x) = 1 + x + 5*x^2 + 46*x^3 + 597*x^4 + 9791*x^5 +...

A(x)^3 = 1 + 3*x + 18*x^2 + 169*x^3 + 2157*x^4 + 34548*x^5 +...

log(1+x*A(x)^3) = x + 5*x^2/2 + 46*x^3/3 + 597*x^4/4 + 9791*x^5/5 +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*deriv(log(1+x*Ser(A)^3)+x*O(x^n))); polcoeff(A, n)}

CROSSREFS

Cf. variants: A159606, A159607.

Sequence in context: A112029 A295544 A058478 * A167559 A121631 A071214

Adjacent sequences:  A159605 A159606 A159607 * A159609 A159610 A159611

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 16 2009

STATUS

approved

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Last modified October 14 14:42 EDT 2019. Contains 328019 sequences. (Running on oeis4.)