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A225095 The number of new maxima over all length n sequences on {1,2,...,n}. 1

%I

%S 0,1,5,41,444,5979,96375,1810297,38845520,937702437,25154615815,

%T 742476758297,23915618605956,834831863473087,31395048114431183,

%U 1265451184688113105,54426870391856267072,2488054366709505840265,120468464465317265258991,6158924799179729969013985

%N The number of new maxima over all length n sequences on {1,2,...,n}.

%H Alois P. Heinz, <a href="/A225095/b225095.txt">Table of n, a(n) for n = 0..150</a>

%e a(2) = 5 because in the length 2 sequences on {1,2}: (1',1), (1',2'), (2',1), (2',2) there are 5 new maxima indicated with '.

%p b:= proc(n, i) option remember; if i<2 then [i$j=1..n]

%p else b(n, i-1); add([0$t=1..j-1, add(%[h], h=1..j)+

%p (j-1)^(i-1), %[t]$t=j+1..n], j=1..n) fi

%p end:

%p a:= n-> add(i, i=b(n, n)):

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Apr 28 2013

%t f[x_List]:=Length[Union[Rest[FoldList[Max,0,x]]]];Table[Total[Map[f,Tuples[Range[1,n],n]]],{n,1,6}]

%Y Cf. A000254 (analogous sequence for permutations).

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Apr 27 2013

%E More terms from _Alois P. Heinz_, Apr 28 2013

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Last modified September 17 13:00 EDT 2019. Contains 327131 sequences. (Running on oeis4.)