This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086115 #20 Dec 02 2024 16:31:15 %S A086115 10,100,390,1080,2470,4980,9170,15760,25650,39940,59950,87240,123630, %T A086115 171220,232410,309920,406810,526500,672790,849880,1062390,1315380, %U A086115 1614370,1965360,2374850,2849860,3397950,4027240,4746430,5564820 %N A086115 Number of 5 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing. %H A086115 Don Coppersmith, <a href="https://research.ibm.com/haifa/ponderthis/challenges/March2004.html">Ponder This: IBM Research Monthly Puzzles, March 2004 challenge</a> %H A086115 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1). %F A086115 a(n) = (1/6)*n*(n^4+10*n^3+35*n^2+50*n-36). More generally, number of m X n (0, 1) matrices such that each row and each column is increasing or decreasing is 2*n*(2*binomial(n+m-1, n)-m) = 4/Beta(m, n)-2*m*n. %F A086115 G.f.: -10*x*(x^4-4*x^3+6*x^2-4*x-1) / (x-1)^6. [_Colin Barker_, Feb 22 2013] %Y A086115 Cf. A032260, A016742, A086113, A086114. %K A086115 nonn,easy %O A086115 1,1 %A A086115 _Vladimir Baltic_, _Vladeta Jovovic_, Jul 10 2003