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 A324632 Number of permutations p of [n] such that five is the maximum of the number of elements in any integer interval [p(i)..i+n*[i

%I #8 Mar 10 2019 11:43:00

%S 76,185,435,1001,2299,5320,12277,28337,65469,151401,350368,811513,

%T 1881187,4364213,10131903,23537656,54713385,127248885,296086085,

%U 689224889,1604944676,3738477553,8710572523,20300163281,47319366179,110319510400,257234285829,599872668089

%N Number of permutations p of [n] such that five is the maximum of the number of elements in any integer interval [p(i)..i+n*[i<p(i)]].

%H Alois P. Heinz, <a href="/A324632/b324632.txt">Table of n, a(n) for n = 5..2000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-3,-6,-8,4,14,16,10,1,-3,-3,-1).

%F G.f.: -x^5 *(41*x^12 +136*x^11 +167*x^10 +14*x^9 -397*x^8 -765*x^7 -807*x^6 -445*x^5 +128*x^4 +261*x^3 +196*x^2 +43*x -76) / ((x+1) *(x^3+x^2+x-1) *(x^4+x^3+x^2+x-1) *(x^5-2*x^3-2*x+1)).

%Y Column k=5 of A324563.

%K nonn,easy

%O 5,1

%A _Alois P. Heinz_, Mar 09 2019

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