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%I #11 Jan 29 2020 19:34:53
%S 0,0,0,0,0,0,420,154637,20368816,1775801814,124151410020,
%T 7596257673279,426319554841752,22564352299016528,1146221298547133380,
%U 56531610963314602401,2728475248127447671008,129586638359127411410442,6080467290450346517206500,282689089820505452872162403
%N Number of 10-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="/A059951/b059951.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = (1/10!)*(45^n - 10*36^n - 45*29^n + 90*28^n + 360*22^n - 480*21^n + 630*17^n - 2520*16^n + 2100*15^n - 3780*12^n + 10080*11^n - 6552*10^n - 3150*9^n + 18900*8^n - 31500*7^n + 28560*6^n - 46620*5^n + 27720*4^n + 85560*3^n - 146160*2^n + 83520).
%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^7*(5467233152463667200*x^14 -6460773223081605120*x^13 +3312489509664336576*x^12 -965946275708647680*x^11 +175045400422088532*x^10 -19853467917718628*x^9 +1255863452001343*x^8 -11591551437545*x^7 -5424120630669*x^6 +520759916751*x^5 -24697320639*x^4 +659527325*x^3 -8843563*x^2 +25697*x +420) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(11*x -1)*(12*x -1)*(15*x -1)*(16*x -1)*(17*x -1)*(21*x -1)*(22*x -1)*(28*x -1)*(29*x -1)*(36*x -1)*(45*x -1)). - _Colin Barker_, Jul 09 2013
%Y Column k=10 of A059443.
%Y Cf. A002718.
%K easy,nonn
%O 1,7
%A _Vladeta Jovovic_, Feb 14 2001
%E More terms from _Colin Barker_, Jul 09 2013
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