A032265 Number of ways to partition n labeled elements into pie slices of at least 2 elements allowing the pie to be turned over.

1, 0, 1, 1, 4, 11, 41, 162, 925, 5945, 47017, 402788, 3895937, 40556595, 461544253, 5625446270, 73716523405, 1028179882589, 15257484239777, 239529471989352, 3971376169852777, 69288230115817655, 1269563315949912469, 24366794306903776610, 488969030312192567573

Offset: 0

Author

Christian G. Bower

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• C. G. Bower, Transforms (2)

Programs

PARI

seq(n)={my(p=exp(x + O(x*x^n))-x-1); Vec(1 + serlaplace(p + p^2/2 - log(1-p))/2)} \\ Andrew Howroyd, Sep 12 2018

Formula

"DIJ" (bracelet, indistinct, labeled) transform of 0, 1, 1, 1, ...

E.g.f.: 1 + (g(x) + g(x)^2/2 - log(1-g(x)))/2 where g(x) = exp(x) - x - 1. - Andrew Howroyd, Sep 12 2018

Extensions

a(0)=1 prepended and terms a(22) and beyond from Andrew Howroyd, Sep 12 2018