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

0,5

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

C. G. Bower, Transforms (2)

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

Prog

(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

Crossrefs

Sequence in context: A214239 A278989 A000296 * A320155 A260320 A151273

Adjacent sequences: A032262 A032263 A032264 * A032266 A032267 A032268

Keyword

nonn

Author

Christian G. Bower

Extensions

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

Status

approved