A059950 - OEIS

%I #14 Jan 29 2020 19:34:01

%S 0,0,0,0,0,15,8456,954213,66253552,3622342095,172672602432,

%T 7557346901841,312733696544984,12456923582109435,483124650731622328,

%U 18383758048494864909,689931203330381971296,25630900118611348761735,945025181750878420241744,34647077709586498046291817

%N Number of 9-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="/A059950/b059950.txt">Table of n, a(n) for n = 1..200</a>

%F a(n)=(1/9!)*(36^n -9*28^n -36*22^n +72*21^n +252*16^n -336*15^n +378*12^n -1512*11^n +1260*10^n -1890*8^n +5040*7^n -4536*6^n +7560*5^n -8820*4^n -11256*3^n +28728*2^n -19152).

%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.: x^6*(69766476595200*x^11 -73112128911360*x^10 +31807557729984*x^9 -7437208397056*x^8 +993276127572*x^7 -70229555428*x^6 +1198328731*x^5 +199609307*x^4 -16366808*x^3 +505224*x^2 -5351*x -15) / ((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)*(12*x -1)*(15*x -1)*(16*x -1)*(21*x -1)*(22*x -1)*(28*x -1)*(36*x -1)). - _Colin Barker_, Jul 09 2013

%Y Column k=9 of A059443.

%Y Cf. A002718.

%K easy,nonn

%O 1,6

%A _Vladeta Jovovic_, Feb 14 2001