A159608 G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x*A(x)^3).

1, 1, 5, 46, 597, 9791, 191876, 4348394, 111561125, 3192096511, 100729014305, 3474750994936, 130094553648612, 5254546985647116, 227771218849108212, 10548385893161367506, 519835256567911242341, 27164324421130818956039

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: A295544 A058478 A367256 * A167559 A367154 A121631

Adjacent sequences: A159605 A159606 A159607 * A159609 A159610 A159611

Keyword

nonn

Author

Paul D. Hanna, May 16 2009

Status

approved