%I #15 Jan 29 2020 19:42:14

%S 0,0,0,0,40,3306,131876,3961356,103290096,2488179582,57162274972,

%T 1274774473632,27887396866472,602352276704178,12899161619186388,

%U 274612697648135028,5822592730060070368,123107330974129584294

%N Number of 7-block bicoverings of an n-set.

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.

%H Vincenzo Librandi, <a href="/A059948/b059948.txt">Table of n, a(n) for n = 1..200</a>

%F a(n)=(1/7!) * (21^n -7*15^n -21*11^n +42*10^n +105*7^n -140*6^n +105*5^n -420*4^n +35*3^n +1050*2^n -1050).

%F The number of m-block bicoverings of an n-set is [x^m*y^n] 1/n!*exp(-x-1/2*x^2*(exp(y)-1)) * sum(i>=0, x^i/i! * exp(binomial(i, 2)*y) ) where [x^m*y^n] extracts the coefficient of x^m*y^n, see Goulden/Jackson p.203.

%F G.f.: 2*x^5*(5197500*x^6-4601880*x^5+1501221*x^4-219455*x^3+12587*x^2+47*x-20) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(10*x-1)*(11*x-1)*(15*x-1)*(21*x-1)). - _Colin Barker_, Jul 07 2013

%Y Column k=7 of A059443.

%Y Cf. A002718.

%K easy,nonn

%O 1,5

%A _Vladeta Jovovic_, Feb 14 2001