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%I #17 Mar 02 2023 13:48:51
%S 43,4520,244035,10418070,401861943,14778678180,530817413155,
%T 18837147108890,664260814445943,23345018969140440,818942064306004275,
%U 28699514624047140510,1005201938765467579543,35196266296400319440300
%N Number of 7-block tricoverings of an n-set.
%C A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.
%H Andrew Howroyd, <a href="/A060485/b060485.txt">Table of n, a(n) for n = 4..200</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (110, -4991, 124120, -1887459, 18470550, -118758569, 501056740, -1355000500, 2223560000, -1973160000, 705600000).
%F a(n) = (1/7!)*(35^n - 7*20^n - 21*15^n + 42*10^n + 105*8^n + 105*7^n + 70*5^n - 945*4^n - 525*3^n + 2450*2^n - 1470).
%F E.g.f. for k-block tricoverings of an n-set is exp(-x+x^2/2+(exp(y)-1)*x^3/3)*Sum_{k=0..infinity}x^k/k!*exp(-1/2*x^2*exp(k*y))*exp(binomial(k, 3)*y).
%F G.f.: x^4*(27300000*x^7 +9288000*x^6 -17908650*x^5 +6008735*x^4 -796380*x^3 +38552*x^2 +210*x -43) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(7*x -1)*(8*x -1)*(10*x -1)*(15*x -1)*(20*x -1)*(35*x -1)). - _Colin Barker_, Jan 12 2013
%Y Column k=7 of A060487.
%Y Cf. A006095, A060483, A060484, A060486, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.
%K nonn,easy
%O 4,1
%A _Vladeta Jovovic_, Mar 20 2001
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