

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



FORMULA

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


MATHEMATICA

a[0] = a[1] = 1; a[n_] := 2^(n2) + HurwitzLerchPhi[1/2, 1n, 0]/2;


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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



