A144008 E.g.f. satisfies: A'(x) = (1 + x*A(x))^3 with A(0)=1.

1, 1, 3, 12, 69, 504, 4455, 46512, 558873, 7599744, 115401915, 1935368640, 35529636285, 708677828352, 15261101987391, 352891976935680, 8721014464717425, 229385791746109440, 6398158947146344755

Offset

0,3

Comments

Compare the definition of the e.g.f. A(x) to the trivial statement:

if F(x) = 1/(1-x) then F'(x) = (1 + x*F(x))^2.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..295

Formula

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

a(n) ~ n^n / (exp(n) * r^(n+2)), where r = 0.628168728379601723852469... - Vaclav Kotesovec, Feb 24 2014

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. A144009, A245247, A245248, A245249.

Sequence in context: A295762 A375811 A375807 * A244610 A187007 A102078

Adjacent sequences: A144005 A144006 A144007 * A144009 A144010 A144011

Keyword

nonn

Author

Paul D. Hanna, Sep 10 2008

Status

approved