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 A192009 Modified cyclic phone booth sequence: number of ways to occupy n labeled phone booths in a circle one by one, each time picking a phone booth adjacent to the smallest number of previously occupied phone booths. 3
 1, 2, 6, 8, 40, 168, 504, 3456, 15552, 97920, 620928, 4465152, 31449600, 273369600, 2172096000, 20968243200, 192753561600, 2032260710400, 20942298316800, 243270107136000, 2758764950323200, 34958441123020800, 434690126954496000, 5946571752210432000, 80503989505228800000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Max Alekseyev, Table of n, a(n) for n = 1..100 FORMULA For n > 1, a(n) = n * Sum (m+k-1)!*binomial(m+k,m)*2^k*k!*(m+k)!, where the sum is taken over nonnegative m,k such that 2*m+3*k = n. - Max Alekseyev, Sep 11 2016 a(n) = n * A276657(n). - Max Alekseyev, Sep 11 2016 EXAMPLE For n=4, the A192009(n) = 6 ways of picking the phone booths are (1, 3, 2, 4), (1, 3, 4, 2), (2, 4, 1, 3), (2, 4, 3, 1), (3, 1, 2, 4), (3, 1, 4, 2), (4, 2, 1, 3), (4, 2, 3, 1). MAPLE A192009 := proc(n)     local a, k, m;     if n = 1 then         return 1;     end if;     a := 0 ;     for k from 0 to n/3 do         m := (n-3*k)/2 ;         if type (m, 'integer') then             a := a+(m+k-1)!*binomial(m+k, m)*2^k*k!*(m+k)! ;         end if;     end do:     a*n ; end proc: seq(A192009(n), n=1..20) ; # R. J. Mathar, Sep 17 2016 MATHEMATICA r[n_] := {ToRules[Reduce[m >= 0 && k >= 0 && 2m+3k == n, {m, k}, Integers] ]}; f[{m_, k_}] := (m+k-1)!*Binomial[m + k, m]*2^k*k!*(m+k)!; a[n_] := n*Total[f /@ ({m, k} /. r[n])]; a = 1; Array[a, 25] (* Jean-François Alcover, Sep 13 2016, after Max Alekseyev *) PROG (PARI) { A192009(n) = my(r, k); if(n==1, return(1)); r=0; forstep(m=lift(Mod(n, 3)/2), n\2, 3, k=(n-2*m)\3; r+=(m+k-1)!*binomial(m+k, m)*2^k*k!*(m+k)!); r*n; } \\ Max Alekseyev, Sep 11 2016 CROSSREFS Cf. A095236, A192008, A192009, A276657. Sequence in context: A327271 A335111 A095239 * A065953 A118211 A050552 Adjacent sequences:  A192006 A192007 A192008 * A192010 A192011 A192012 KEYWORD nonn AUTHOR Jens Voß, Jun 21 2011 EXTENSIONS Terms a(15) onward from Max Alekseyev, Sep 11 2016 STATUS approved

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)