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

0,3

Links

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

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

Example

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).

Prog

(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), ", "))

Crossrefs

Cf. A112936, A112938, A218168.

Sequence in context: A301434 A232192 A249791 * A195242 A243697 A106273

Adjacent sequences: A215645 A215646 A215647 * A215649 A215650 A215651

Keyword

nonn

Author

Paul D. Hanna, Mar 09 2013

Status

approved