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A062868 Number of permutations of degree n with barycenter 0. 16


%S 1,1,2,4,14,46,282,1394,12658,83122,985730,8012962,116597538,

%T 1127575970,19410377378,217492266658,4320408974978,55023200887938,

%U 1238467679662722,17665859065690754,444247724347355554,7015393325151055906,194912434760367113570,3375509056735963889634

%N Number of permutations of degree n with barycenter 0.

%C The barycenter or signcenter of a permutation is the sum of the signs of the difference between initial and final positions of the objects.

%H Maxwell Jiang, <a href="/A062868/b062868.txt">Table of n, a(n) for n = 0..150</a>

%F a(n) = Sum_{k=0..floor(n/2)} binomial(n, n-2*k)*A320337(k). - _Maxwell Jiang_, Dec 19 2018 (added by editors)

%e (4,1,3,5,2) has difference (3,-1,0,1,-3) and signs (1,-1,0,1,-1) with total 0.

%p b:= proc(s, t) option remember; (n-> `if`(abs(t)>n, 0, `if`(n=0, 1,

%p add(b(s minus {j}, t+signum(n-j)), j=s))))(nops(s))

%p end:

%p a:= n-> b({$1..n}, 0):

%p seq(a(n), n=0..14); # _Alois P. Heinz_, Jul 31 2018

%Y Column k=0 of A062866 or of A062867.

%Y Cf. A179567, A196687, A196688, A320337.

%K nice,nonn

%O 0,3

%A _Olivier GĂ©rard_, Jun 26 2001

%E One more term from _Vladeta Jovovic_, Jun 28 2001

%E a(11)-a(14) from _Hugo Pfoertner_, Sep 23 2004

%E a(15)-a(18) from _R. H. Hardin_, Jul 18 2010

%E a(19)-a(22) from _Kyle G Hess_, Jul 30 2018

%E a(0)=1 prepended by _Alois P. Heinz_, Jul 30 2018

%E Terms a(23) and beyond from _Maxwell Jiang_, Dec 19 2018

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Last modified September 18 23:06 EDT 2020. Contains 337174 sequences. (Running on oeis4.)