A032219 Number of ways to partition n labeled elements into pie slices of different sizes allowing the pie to be turned over.

1, 1, 1, 4, 5, 16, 82, 169, 541, 2272, 43166, 99859, 479030, 2089751, 13714261, 493866559, 1397727901, 7786145776, 39662742502, 252997758007, 2026338881050, 131040136520017, 427809641611111, 2813929521468817

Offset

0,4

Links

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

C. G. Bower, Transforms (2)

Formula

"DGJ" (bracelet, element, labeled) transform of 1, 1, 1, 1...

Prog

(PARI) seq(n)=[subst(serlaplace(p/y + polcoeff(p, 1) + polcoeff(p, 2)), y, 1)/2 | p <- Vec(y-1+serlaplace(prod(k=1, n, (1 + x^k*y/k! + O(x*x^n)))))] \\ Andrew Howroyd, Sep 11 2018

Crossrefs

Sequence in context: A013628 A127007 A007837 * A032144 A032049 A258063

Adjacent sequences: A032216 A032217 A032218 * A032220 A032221 A032222

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended by Andrew Howroyd, Sep 11 2018

Status

approved