|
%I #13 Jan 29 2020 19:42:26
%S 0,0,0,0,0,535,51640,2771685,114713760,4127125695,136631722920,
%T 4292250804985,130278290187760,3863262740532195,112733098867629240,
%U 3252644718804860925,93093809127731630400,2649006256251644780935
%N Number of 8-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="/A059949/b059949.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = (1/8!)*(28^n - 8*21^n - 28*16^n + 56*15^n + 168*11^n - 224*10^n + 210*8^n - 840*7^n + 700*6^n - 840*5^n + 1925*4^n + 1064*3^n - 5460*2^n + 4368).
%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 G.f.: -5*x^6*(3390266880*x^8 -3368778336*x^7 +1334596314*x^6 -268312855*x^5 +27919999*x^4 -1171492*x^3 -29534*x^2 +4331*x -107) / ((x -1)*(2*x -1)*(3*x- 1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(10*x -1)*(11*x -1)*(15*x -1)*(16*x -1)*(21*x -1)*(28*x -1)). - _Colin Barker_, Jul 08 2013
%Y Column k=8 of A059443.
%Y Cf. A002718.
%K easy,nonn
%O 1,6
%A _Vladeta Jovovic_, Feb 14 2001
| 