A144013 E.g.f. satisfies: A'(x) = 1 + x*A(x)^3 where A(0) = 1.

1, 1, 1, 6, 27, 168, 1395, 12744, 136521, 1672704, 22659993, 340472160, 5605239123, 100154133504, 1933748430939, 40097756280960, 888588043228305, 20962928129900544, 524479633529596209, 13871161113800394240

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..286

Formula

E.g.f. satisfies: A(x) = 1 + Integral [1 + x*A(x)^3] dx.

a(n) ~ n^n / (exp(n) * r^(n+1)), where r = 0.69974580613381637... - Vaclav Kotesovec, Feb 24 2014

Example

E.g.f.: A(x) = 1 + x + x^2/2! + 6*x^3/3! + 27*x^4/4! + 168*x^5/5! +...
A(x)^3 = 1 + 3*x + 9*x^2/2! + 42*x^3/3! + 279*x^4/4! + 2124*x^5/5! +...
x*A(x)^3 = x + 6*x^2/2! + 27*x^3/3! + 168*x^4/4! + 1395*x^5/5! +...
A'(x) = 1 + x + 6*x^2/2! + 27*x^3/3! + 168*x^4/4! + 1395*x^5/5! +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(1+x*(A+x*O(x^n))^3)); n!*polcoeff(A, n)}

Crossrefs

Cf. A144012, A144014.

Sequence in context: A087297 A117336 A202766 * A318565 A092854 A223557

Adjacent sequences: A144010 A144011 A144012 * A144014 A144015 A144016

Keyword

nonn

Author

Paul D. Hanna, Sep 10 2008

Status

approved