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A283026 Number of inequivalent 4 X 4 matrices with entries in {1,2,3,..,n} up to row permutations.

%I A283026 #17 Dec 07 2018 14:48:40
%S A283026 0,1,3876,1929501,183181376,6419043125,118091211876,1388168405001,
%T A283026 11745311589376,77279801651001,416916712502500,1915356782994501,
%U A283026 7705740009485376,27731516944463501,90762229896563876,273716119247180625,768684707117285376,2027695320242670001
%N A283026 Number of inequivalent 4 X 4 matrices with entries in {1,2,3,..,n} up to row permutations.
%C A283026 Cycle index of symmetry group S4 acting on the 16 entries is (6*s(2)^4s(1)^8 + 8*s(3)^4s(1)^4 + 3*s(2)^8 + 6*s(4)^4 + s(1)^{16})/24.
%F A283026 a(n) = n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24.
%F A283026 From _Chai Wah Wu_, Dec 07 2018: (Start)
%F A283026 a(n) = 17*a(n-1) - 136*a(n-2) + 680*a(n-3) - 2380*a(n-4) + 6188*a(n-5) - 12376*a(n-6) + 19448*a(n-7) - 24310*a(n-8) + 24310*a(n-9) - 19448*a(n-10) + 12376*a(n-11) - 6188*a(n-12) + 2380*a(n-13) - 680*a(n-14) + 136*a(n-15) - 17*a(n-16) + a(n-17) for n > 16.
%F A283026 G.f.: -x*(x + 1)*(x^14 + 3858*x^13 + 1859887*x^12 + 149046428*x^11 + 3415692141*x^10 + 29161611758*x^9 + 104450960739*x^8 + 161533106376*x^7 + 104450960739*x^6 + 29161611758*x^5 + 3415692141*x^4 + 149046428*x^3 + 1859887*x^2 + 3858*x + 1)/(x - 1)^17. (End)
%e A283026 For n=2 we get a(2)=3876 inequivalent 4x4 binary matrices up to row permutations.
%t A283026 Table[n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24,{n,0,30}]
%o A283026 (PARI) a(n) = n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24; \\ _Indranil Ghosh_, Feb 27 2017
%o A283026 (Python) def A283026(n) : return n**4*(n**4 + 1)*(n**4 + 2)*(n**4 + 3)/24 # _Indranil Ghosh_, Feb 27 2017
%Y A283026 Cf. A282613, A282614, A283027, A283028, A283029, A283031, A283032, A283033. A283030 (5x5 version). A282612 (3x3 version). A037270 (2x2 version).
%K A283026 easy,nonn
%O A283026 0,3
%A A283026 _David Nacin_, Feb 27 2017