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

%I A225095 #23 Jul 22 2020 18:44:30
%S A225095 0,1,5,41,444,5979,96375,1810297,38845520,937702437,25154615815,
%T A225095 742476758297,23915618605956,834831863473087,31395048114431183,
%U A225095 1265451184688113105,54426870391856267072,2488054366709505840265,120468464465317265258991,6158924799179729969013985
%N A225095 The number of new maxima over all length n sequences on {1,2,...,n}.
%H A225095 Alois P. Heinz, <a href="/A225095/b225095.txt">Table of n, a(n) for n = 0..200</a>
%e A225095 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 A225095 b:= proc(n, i) option remember; if i<2 then [i$j=1..n]
%p A225095       else b(n, i-1); add([0$t=1..j-1, add(%[h], h=1..j)+
%p A225095            (j-1)^(i-1), %[t]$t=j+1..n], j=1..n) fi
%p A225095     end:
%p A225095 a:= n-> add(i, i=b(n, n)):
%p A225095 seq(a(n), n=0..25);  # _Alois P. Heinz_, Apr 28 2013
%t A225095 f[x_List]:=Length[Union[Rest[FoldList[Max,0,x]]]];Table[Total[Map[f,Tuples[Range[1,n],n]]],{n,1,6}]
%Y A225095 Cf. A000254 (analogous sequence for permutations), A336482.
%K A225095 nonn
%O A225095 0,3
%A A225095 _Geoffrey Critzer_, Apr 27 2013
%E A225095 More terms from _Alois P. Heinz_, Apr 28 2013