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%I #21 Sep 23 2023 10:42:09
%S 1,665,106819,10365005,805351531,56294206205,3735873535339,
%T 241600284318365,15423235216318411,978180744322139645,
%U 61834480769377286059,3902270609960140639325,246057483524862034206091,15508484277325946034039485,977254123876968508188975979
%N Number of connected relations.
%H T. D. Noe, <a href="/A093733/b093733.txt">Table of n, a(n) for n = 1..100</a>
%H Goran Kilibarda and Vladeta Jovovic, <a href="https://arxiv.org/abs/1411.4187">Enumeration of some classes of T_0-hypergraphs</a>, arXiv:1411.4187 [math.CO], 2014.
%H G. Kreweras, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k480296q/f583.image">Inversion des polynômes de Bell bidimensionnels et application au dénombrement des relations binaires connexes</a>, C. R. Acad. Sci. Paris Ser. A-B 268 1969 A577-A579.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (-195, 15886, -726290, 20952193, -403792115, 5336718048, -48588590600, 299693200656, -1195947048240, 2785165036416, -2872859996160).
%F a(n) = 63^n - 6*32^n - 15*18^n + 30*17^n - 10*14^n + 120*11^n - 120*10^n + 30*9^n - 270*8^n + 360*7^n - 120*6^n.
%F G.f.: x*(96368590080*x^9 + 27682953984*x^8 - 13185435000*x^7 + 774468980*x^6 + 143028190*x^5 - 19071533*x^4 + 626800*x^3 + 6970*x^2 - 470*x - 1) / ((6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(11*x -1)*(14*x -1)*(17*x -1)*(18*x -1)*(32*x -1)*(63*x -1)). - _Colin Barker_, Jul 07 2013
%t Table[63^n-6*32^n-15*18^n+30*17^n-10*14^n+120*11^n-120*10^n+30*9^n-270*8^n+360*7^n-120*6^n, {n,1,25}] (* _G. C. Greubel_, Oct 06 2017 *)
%t CoefficientList[Series[x (96368590080x^9+27682953984x^8-13185435000x^7+774468980x^6+ 143028190x^5-19071533x^4+626800x^3+6970x^2-470x-1)/((6x-1)(7x-1)(8x-1)(9x-1)(10x-1)(11x-1)(14x-1)(17x-1)(18x-1)(32x-1)(63x-1)),{x,0,20}],x] (* or *) LinearRecurrence[{195,-15886,726290,-20952193,403792115,-5336718048,48588590600,-299693200656,1195947048240,-2785165036416,2872859996160},{0,1,665,106819,10365005,805351531,56294206205,3735873535339,241600284318365,15423235216318411,978180744322139645},20] (* _Harvey P. Dale_, Sep 23 2023 *)
%o (PARI) for(n=1,25, print1(63^n-6*32^n-15*18^n+30*17^n-10*14^n+120*11^n-120*10^n+30*9^n-270*8^n+360*7^n-120*6^n, ", ")) \\ _G. C. Greubel_, Oct 06 2017
%Y Cf. A001047, A002501, A002502, A005333, A093732.
%K nonn,easy
%O 1,2
%A Goran Kilibarda and _Vladeta Jovovic_, Apr 14 2004
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