A038038 Number of labeled dyslexic rooted compound windmills with n nodes.

1, 2, 9, 64, 635, 8142, 128394, 2405784, 52237296, 1289735280, 35680244490, 1093124356560, 36734913680244, 1343439671120904, 53111942243599680, 2256996523715952480, 102589277119862240160, 4966450613410762025280, 255110144003301741908832

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for sequences related to mobiles

Formula

Divides by n and shifts left under "DIJ" (bracelet, indistinct, labeled) transform.

E.g.f: series reversion of 2*x/(2 + x + x^2/2 - log(1-x)). - Andrew Howroyd, Sep 19 2018

a(n) ~ sqrt(s) * (2 - s^2)^(n + 1/2) * n^n / (sqrt(2 - 2*s + s^2) * n * 2^n * (1-s)^(n - 1/2) * exp(n)), where s = 0.7579492001963653206343844374776312472163... is the root of the equation 4 - 6*s - s^2 + s^3 - 2*(1-s)*log(1-s) = 0. - Vaclav Kotesovec, Apr 21 2020

Mathematica

m = 20;
CoefficientList[InverseSeries[2*x/(2 + x + x^2/2 - Log[1 - x]) + O[x]^m], x]*Range[0, m - 1]! // Rest (* Jean-François Alcover, Sep 08 2019 *)

Prog

(PARI) Vec(serlaplace(serreverse(2*x/(2 + x + x^2/2 - log(1-x + O(x^20)))))) \\ Andrew Howroyd, Sep 19 2018

Crossrefs

Cf. A032289.

Sequence in context: A000169 A112319 A232552 * A368790 A048801 A152915

Adjacent sequences: A038035 A038036 A038037 * A038039 A038040 A038041

Keyword

nonn,eigen

Author

Christian G. Bower

Extensions

Terms a(17) and beyond from Andrew Howroyd, Sep 19 2018

Status

approved