The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
C. G. Bower, Transforms (2)
FORMULA
a(n) = 2^(n-2) + A000670(n-1) for n >= 2. - N. J. A. Sloane, Jan 17 2008
a(n) = 2^(n-1) + Sum_{k >= 3} Stirling_2(n,k)*(k-1)!/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(1-g(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 .. 3--4 . 34 .. 4
.(3)....(6)...(3)..(4)...(1) Total a(4) = 17
MATHEMATICA
a[0] = a[1] = 1; a[n_] := 2^(n-2) + HurwitzLerchPhi[1/2, 1-n, 0]/2;
Array[a, 20, 0] (* Jean-François Alcover, Aug 26 2019 *)
PROG
(PARI) seq(n)={my(p=exp(x + O(x*x^n))-1); Vec(1 + serlaplace(p + p^2/2 - log(1-p))/2)} \\ Andrew Howroyd, Sep 12 2018
CROSSREFS
Row sums of triangle A133800.
Sequence in context: A098540 A079574 A363002 * A144259 A191799 A079805
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Jan 17 2008
a(0)=1 prepended by Andrew Howroyd, Sep 12 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 18 15:47 EDT 2024. Contains 373481 sequences. (Running on oeis4.)