A032264 Number of ways to partition n labeled elements into pie slices of odd sizes allowing the pie to be turned over.

1, 1, 1, 2, 7, 23, 136, 872, 6952, 62813, 641536, 7277342, 90825472, 1236592403, 18239374336, 289719603812, 4930706056192, 89509486108793, 1726465695809536, 35259035421020282, 760088211047514112, 17247810060070731983, 410954011551070683136, 10257838886120978286752

Offset

0,4

Links

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

C. G. Bower, Transforms (2)

Formula

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

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

Prog

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

Crossrefs

Sequence in context: A375130 A332802 A002494 * A139522 A163158 A355981

Adjacent sequences: A032261 A032262 A032263 * A032265 A032266 A032267

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Sep 12 2018

Status

approved