A250889 G.f. A(x) satisfies: x = A(x) * (1 + 2*A(x)) * (1 - 3*A(x)).

1, 1, 8, 35, 248, 1554, 11184, 79431, 591800, 4445870, 34121360, 264561310, 2076527152, 16438316260, 131209328736, 1054363402863, 8524604038968, 69288162549270, 565870782325200, 4641105293930490, 38211609118671120, 315703155339764220, 2616604440745545120

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Formula

G.f.: Series_Reversion(x - x^2 - 6*x^3).

a(n) ~ 2^(n - 3/2) * (28 + 19*sqrt(19))^(n - 1/2) / (19^(1/4) * sqrt(Pi) * n^(3/2) * 5^(2*n - 1)). - Vaclav Kotesovec, Aug 22 2017

Example

G.f.: A(x) = x + x^2 + 8*x^3 + 35*x^4 + 248*x^5 + 1554*x^6 + 11184*x^7 +...
Related expansions.
A(x)^2 = x^2 + 2*x^3 + 17*x^4 + 86*x^5 + 630*x^6 + 4164*x^7 +...
A(x)^3 = x^3 + 3*x^4 + 27*x^5 + 154*x^6 + 1170*x^7 + 8127*x^8 +...
where x = A(x) - A(x)^2 - 6*A(x)^3.

Mathematica

Rest[CoefficientList[InverseSeries[Series[x - x^2 - 6*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *)

Prog

(PARI) {a(n)=polcoeff(serreverse(x - x^2 - 6*x^3 +x^2*O(x^n)), n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A192257 A297609 A000426 * A200312 A339325 A089698

Adjacent sequences: A250886 A250887 A250888 * A250890 A250891 A250892

Keyword

nonn

Author

Paul D. Hanna, Nov 28 2014

Status

approved