%I #17 Jan 30 2020 14:25:16
%S 0,0,0,0,125,722,2565,7180,17335,37750,76093,144340,260590,451440,
%T 755040,1224964,1935050,2985380,4509590,6683720,9736835,13963670,
%U 19739575,27538060,37951265,51713706,69729675,93104700,123181500
%N Number of 5-block ordered bicoverings of an unlabeled n-set.
%H Harry J. Smith, <a href="/A060093/b060093.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n) = binomial(n+9, 9) - 5*binomial(n+5, 5) - 10*binomial(n+3, 3) + 20*binomial(n+2, 2) + 30*binomial(n+1, 1) - 60*binomial(n, 0) + 24*binomial(n-1, -1).
%F G.f.: y^4*(-528*y + 125 + 970*y^2 - 980*y^3 + 570*y^4 - 180*y^5 + 24*y^6)/(-1 + y)^10.
%F E.g.f. for k-block ordered bicoverings of an unlabeled n-set is exp(-x - x^2/2*y/(1 - y))*Sum_{k>=0} 1/(1 - y)^binomial(k, 2)*x^k/k!.
%F a(n) = (n-1) *(n-2) *(n-3) *(n^6 + 51*n^5 + 1165*n^4 + 15885*n^3 + 130954*n^2 + 660504*n + 1451520)/ 362880, n > 0. - _R. J. Mathar_, Aug 10 2017
%o (PARI) a(n) = if(n<1, 0, binomial(n + 9, 9) - 5*binomial(n + 5, 5) - 10*binomial(n + 3, 3) + 20*binomial(n + 2, 2) + 30*binomial(n + 1, 1) - 60*binomial(n, 0) + 24*binomial(n - 1, -1)) \\ _Harry J. Smith_, Jul 01 2009
%Y Column k=5 of A060092.
%Y Cf. A059946, A060090, A060489.
%K nonn,easy
%O 0,5
%A _Vladeta Jovovic_, Feb 26 2001