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A112461 Absolute value of coefficient of term [x^(n-5)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 5. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

%I A112461 #28 Jul 23 2019 14:54:26
%S A112461 5,59,374,1694,6149,19019,52052,129272,296582,636922,1293292,2502604,
%T A112461 4644094,8306914,14382544,24188824,39633715,63428365,99360690,
%U A112461 152642490,230345115,341940885,499969860,720854160,1025884860,1442409540,2005251864,2758398104
%N A112461 Absolute value of coefficient of term [x^(n-5)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 5. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
%H A112461 T. D. Noe and Bruno Berselli, <a href="/A112461/b112461.txt">Table of n, a(n) for n = 5..1004</a>
%H A112461 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A112461 a(n) = ((9n+5)/10!) * Product_{i=-4..4} (n+i).
%F A112461 G.f.: x^5*(5+4*x)/(1-x)^11. - _Colin Barker_, Mar 28 2012
%t A112461 Table[(9n+5)/10! Product[n+i,{i,-4,4}],{n,5,40}] (* _Harvey P. Dale_, Apr 26 2019 *)
%o A112461 (Octave, MATLAB) for n=5:20 a = zeros(n); for i=1:n for j=1:n a(i,j) = max(i,j); end end b = poly(a); b(6) end
%Y A112461 Cf. A000217, A000914, A001844, A112459, A112460, A112462, A112463, A112464.
%K A112461 nonn,easy
%O A112461 5,1
%A A112461 _Paul Max Payton_, Sep 23 2005
%E A112461 Offset changed from 1 to 5, formulas and b-file adapted by _Bruno Berselli_, Mar 29 2012