A250890 G.f. A(x) satisfies: x = A(x) * (1 + 2*A(x)) * (1 - 5*A(x)).

1, 3, 28, 285, 3324, 41286, 537528, 7233633, 99829180, 1405109706, 20092995624, 291094349442, 4263366676632, 63021155618700, 939010901406960, 14088102521345865, 212648697998549820, 3226980657263323170, 49203799749341113800, 753450185890639113030

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

G.f.: Series_Reversion(x - 3*x^2 - 10*x^3).

a(n) ~ 2^(n - 3/2) * 3^(n - 3/4) * (54 + 13*sqrt(39))^(n - 1/2) / (13^(1/4) * sqrt(Pi) * n^(3/2) * 7^(2*n - 1)). - Vaclav Kotesovec, Aug 22 2017

Example

G.f.: A(x) = x + 3*x^2 + 28*x^3 + 285*x^4 + 3324*x^5 + 41286*x^6 +...
Related expansions.
A(x)^2 = x^2 + 6*x^3 + 65*x^4 + 738*x^5 + 9142*x^6 + 118476*x^7 +...
A(x)^3 = x^3 + 9*x^4 + 111*x^5 + 1386*x^6 + 18210*x^7 + 246321*x^8 +...
where x = A(x) - 3*A(x)^2 - 10*A(x)^3.

Mathematica

Rest[CoefficientList[InverseSeries[Series[x - 3*x^2 - 10*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *)

Prog

(PARI) {a(n)=polcoeff(serreverse(x - 3*x^2 - 10*x^3 +x^2*O(x^n)), n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A181069 A239297 A287884 * A199754 A277507 A176335

Adjacent sequences: A250887 A250888 A250889 * A250891 A250892 A250893

Keyword

nonn

Author

Paul D. Hanna, Nov 28 2014

Status

approved