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%I #23 Mar 09 2024 13:00:50
%S 0,0,4,39,280,1815,11284,68859,416560,2509455,15086764,90610179,
%T 543928840,3264374295,19588645444,117539063499,705255937120,
%U 4231600258335,25389795391324,152339353740819,914037866361400,5484232429393575,32905410268988404,197432508689714139
%N Number of 4-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="/A059945/b059945.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,72,-36).
%F a(n) = (1/4!)*(6^n - 4*3^n - 3*2^n + 12).
%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..inf} x^i/i!*exp(binomial(i, 2)*y).
%F a(n) = 12*a(n-1) - 47*a(n-2) + 72*a(n-3) - 36*a(n-4) for n > 4. - _Harvey P. Dale_, Aug 10 2011
%F G.f.: -x^3*(9*x-4) / ((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). - _Colin Barker_, Jan 11 2013
%e There are 4 4-block bicoverings of a 3-set: {{1},{2},{3},{1,2,3}}, {{2},{3},{1,2},{1,3}}, {{1},{3},{1,2},{2,3}} and {{1},{2},{1,3},{2,3}}.
%t With[{c=1/4!},Table[c(6^n-4 3^n-3 2^n+12),{n,20}]] (* or *) LinearRecurrence[ {12,-47,72,-36},{0,0,4,39},20] (* _Harvey P. Dale_, Aug 10 2011 *)
%o (PARI) a(n) = {(1/4!)*(6^n - 4*3^n - 3*2^n + 12)} \\ _Andrew Howroyd_, Jan 29 2020
%Y Column k=4 of A059443.
%Y Cf. A002718.
%K easy,nonn
%O 1,3
%A _Vladeta Jovovic_, Feb 14 2001
%E More terms from _Colin Barker_, Jan 11 2013
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