A215648 G.f. satisfies: A(x) = 1 + x*A(x)^2 + 3*x^2*A'(x)*A(x).

1, 1, 5, 44, 539, 8337, 154632, 3332640, 81711479, 2244563555, 68272834865, 2278102125040, 82749748994500, 3250966816344604, 137371215935579892, 6213234210869600376, 299527133488944917631, 15332761842086151881175, 830648056455231849827895

Offset: 0

Author

Paul D. Hanna, Mar 09 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 5*x^2 + 44*x^3 + 539*x^4 + 8337*x^5 + 154632*x^6 +...
Related expansions:
A(x)^2 = 1 + 2*x + 11*x^2 + 98*x^3 + 1191*x^4 + 18192*x^5 + 333264*x^6 +...
A'(x)*A(x) = 1 + 11*x + 147*x^2 + 2382*x^3 + 45480*x^4 + 999792*x^5 +...
where A(x) = 1 + x*A(x)^2 + 3*x^2*A'(x)*A(x).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..378

Crossrefs

Cf. A112936, A112938, A218168.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+x*deriv(x*A^3)/(A+x*O(x^n)));polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))

Formula

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

a(n) ~ n! * 3^(n+1) / (Pi*exp(1)). - Vaclav Kotesovec, Aug 24 2017

a(0) = 1; a(n) = Sum_{k=0..n-1} (3*k+1) * a(k) * a(n-k-1). - Ilya Gutkovskiy, Sep 05 2024