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

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