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Total number of occurrences of the consecutive step pattern given by the binary expansion of n (where 1=up and 0=down) in all permutations of [n].
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%I #7 Jan 12 2015 10:50:12

%S 0,0,0,1,3,50,270,840,5376,166320,2903040,20956320,191600640,

%T 4203239040,29059430400,119870150400,1598268672000,112634352230400,

%U 4623936565248000,61498356317798400,1773991047628800000,69256610499428352000,1061556242901073920000

%N Total number of occurrences of the consecutive step pattern given by the binary expansion of n (where 1=up and 0=down) in all permutations of [n].

%H Alois P. Heinz, <a href="/A249249/b249249.txt">Table of n, a(n) for n = 0..130</a>

%F a(n) = Sum_{k>0} k*A242783(n,k).

%Y Cf. A242783.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jan 12 2015