%I #26 Mar 09 2024 13:00:34
%S 0,0,0,25,472,6185,70700,759045,7894992,80736625,817897300,8241325565,
%T 82783813112,830046591465,8313655213500,83215436364085,
%U 832626645756832,8329096006484705,83307920631515300,833180902353754605,8332418928963358152,83327847634888960345
%N Number of 5-block bicoverings of an n-set.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
%H Andrew Howroyd, <a href="/A059946/b059946.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (26,-255,1210,-2924,3384,-1440).
%F a(n) = (1/5!)*(10^n - 5*6^n - 10*4^n + 20*3^n + 30*2^n - 60).
%F E.g.f. for m-block bicoverings of an n-set is exp(-x-1/2*x^2*(exp(y)-1))*Sum_{i>=0} (x^i/i!)*exp(binomial(i, 2)*y).
%F G.f.: x^4*(288*x^2-178*x+25) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)*(10*x-1)). - _Colin Barker_, Jan 11 2013
%t With[{c=(1/5!)},Table[c(10^n-5 6^n-10 4^n+20 3^n+30 2^n-60),{n,20}]] (* _Harvey P. Dale_, Apr 21 2011 *)
%o (PARI) a(n) = {(1/5!)*(10^n - 5*6^n - 10*4^n + 20*3^n + 30*2^n - 60)} \\ _Andrew Howroyd_, Jan 29 2020
%Y Column k=5 of A059443.
%Y Cf. A002718.
%K easy,nonn
%O 1,4
%A _Vladeta Jovovic_, Feb 14 2001
%E More terms from _Colin Barker_, Jan 11 2013
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