

A032262


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


2



1, 1, 2, 5, 17, 83, 557, 4715, 47357, 545963, 7087517, 102248075, 1622633597, 28091569643, 526858352477, 10641342978635, 230283190994237, 5315654682014123, 130370767029201437, 3385534663256976395
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OFFSET

0,3


LINKS

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


FORMULA

a(n) = 2^(n2) + A000670(n1) for n >= 2.  N. J. A. Sloane, Jan 17 2008
a(n) = 2^(n1) + Sum_{k >= 3} Stirling_2(n,k)*(k1)!/2 for n >= 1.  N. J. A. Sloane, Jan 17 2008
"DIJ" (bracelet, indistinct, labeled) transform of 1, 1, 1, 1, ... (see Bower link).
E.g.f.: 1 + (g(x) + g(x)^2/2  log(1g(x)))/2 where g(x) = exp(x)  1.  Andrew Howroyd, Sep 12 2018


EXAMPLE

For n = 4 we have the following "pies":
. 1
./ \
2 . 3 . 12 .. 12 . 123 .1234
.\ / .. / \ .(..)..(..)
. 4 .. 34 . 34 .. 4
.(3)....(6)...(3)..(4)...(1) Total a(4) = 17


PROG

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


CROSSREFS

Row sums of triangle A133800.
Sequence in context: A076322 A098540 A079574 * A144259 A191799 A079805
Adjacent sequences: A032259 A032260 A032261 * A032263 A032264 A032265


KEYWORD

nonn


AUTHOR

Christian G. Bower


EXTENSIONS

Edited by N. J. A. Sloane, Jan 17 2008
a(0)=1 prepended by Andrew Howroyd, Sep 12 2018


STATUS

approved



