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%I #12 Sep 03 2018 23:06:54
%S 1,1,4,10,33,91,277,792,2341,6654,18802,51508,138147,359457,910756,
%T 2240915,5365106,12495406,28353714,62725603,135469991,285904968,
%U 590347527,1193817552,2366907846,4605225266,8801576140,16538061290
%N Number of nonnegative integer 5 X 5 matrices with sum of elements equal to n, under row and column permutations.
%H Andrew Howroyd, <a href="/A052367/b052367.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: - (x^86 - 3*x^85 + 9*x^84 + 12*x^83 + 59*x^82 + 116*x^81 + 452*x^80 + 736*x^79 + 2080*x^78 + 3344*x^77 + 7312*x^76 + 11708*x^75 + 21793*x^74 + 32869*x^73 + 55563*x^72 + 79389*x^71 + 123072*x^70 + 168321*x^69 + 243961*x^68 + 319938*x^67 + 438431*x^66 + 553731*x^65 + 724251*x^64 + 885383*x^63 + 1111989*x^62 + 1318149*x^61 + 1600579*x^60 + 1845557*x^59 +
%F 2172889*x^58 + 2444070*x^57 + 2798839*x^56 + 3076865*x^55 + 3436180*x^54 + 3696058*x^53 + 4034590*x^52 + 4250683*x^51 + 4541020*x^50 + 4689359*x^49 + 4909073*x^48 + 4972196*x^47 + 5102026*x^46 + 5069013*x^45 + 5102464*x^44 + 4971700*x^43 + 4909948*x^42 + 4688757*x^41 + 4542211*x^40 + 4249809*x^39 + 4036170*x^38 + 3694857*x^37 + 3438025*x^36 +
%F 3075494*x^35 + 2800760*x^34 + 2442552*x^33 + 2174743*x^32 + 1843864*x^31 + 1602482*x^30 + 1316113*x^29 + 1114023*x^28 + 883313*x^27 + 725930*x^26 + 551915*x^25 + 439662*x^24 + 318308*x^23 + 245205*x^22 + 166823*x^21 + 124009*x^20 + 78506*x^19 + 56071*x^18 + 32361*x^17 + 22208*x^16 + 11357*x^15 + 7673*x^14 + 3221*x^13 + 2294*x^12 + 684*x^11 + 594*x^10 + 59*x^9 + 133*x^8 + 21*x^7 + 18*x^6 - 2*x^4 - 3*x^3 + 9*x^2 - 5*x + 1) divided by (see next line)
%F ((x^20 - 1)*(x^11 - x^10 + x^6 - x^5 + x - 1)*(x^7 - 2*x^6 + x^5 + x^4 - x^3 - x^2 + 2*x - 1)*(x^4 + x^3 + x^2 + x + 1)^4*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^2 + 1)*(x^2 + 1)^5*(x^2 + x + 1)^5*(x + 1)^11*(x - 1)^22).
%Y Row 5 of A318795.
%Y Cf. A002724, A053307, A052365, A052366.
%K nonn
%O 0,3
%A _Vladeta Jovovic_, Mar 08 2000
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