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%I #18 Sep 08 2022 08:44:59
%S 0,1,16,146,955,4905,20907,76851,250530,739612,2009177,5085119,
%T 12109526,27348478,58955082,121956402,243172488,469115187,878387366,
%U 1600751976,2845918041,4946262815,8419256605,14057377245,23055913530,37192403430,59075703351,92488040301
%N Number of 4 X n binary matrices such that any 2 rows have a common 1, up to column permutations.
%D V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
%H T. D. Noe, <a href="/A052388/b052388.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n^10 +110*n^9 +5445*n^8 +160050*n^7 +2906463*n^6 +30644250*n^5 +176659055*n^4 +711220750*n^3 +1781493036*n^2 +4034382840*n +4159814400)/1307674368000.
%F G.f.: -x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16. - _Colin Barker_, Nov 05 2012
%t CoefficientList[Series[-x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16, {x, 0, 50}], x] (* _G. C. Greubel_, Oct 07 2017 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(-x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16)) \\ _G. C. Greubel_, Oct 07 2017
%o (Magma) [n*(n+1)*(n+2)*(n+3)*(n+4)*(n^10 +110*n^9 +5445*n^8 +160050*n^7 +2906463*n^6 +30644250*n^5 +176659055*n^4 +711220750*n^3 +1781493036*n^2 +4034382840*n +4159814400)/1307674368000: n in [0..25]]; // _G. C. Greubel_, Oct 07 2017
%Y Cf. A051588, A051587, A051589.
%K nonn,easy
%O 0,3
%A _Vladeta Jovovic_, Goran Kilibarda, Mar 11 2000
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