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%I #16 Jan 30 2020 14:24:11
%S 0,0,0,0,0,1680,27342,208302,1099602,4636072,16734438,53810484,
%T 158053119,431305959,1106791524,2694914978,6269281305,14010246285,
%U 30208869495,63074014815,127909521180,252581107180,486738385140
%N Number of 7-block ordered bicoverings of an unlabeled n-set.
%H Harry J. Smith, <a href="/A060095/b060095.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = binomial(n+20, n) - 7*binomial(n+14, 14) - 21*binomial(n+10, 10) + 42*binomial(n+9, 9) + 105*binomial(n+6, 6) - 140*binomial(n+5, 5) + 105*binomial(n+4, 4) - 420*binomial(n+3, 3) + 35*binomial(n+2, 2) + 1050*binomial(n+1, 1) - 1050*binomial(n, 0) + 300*binomial(n-1, -1).
%F G.f.: y^5*(-1680 - 7005635*y^7 + 5039622*y^6 - 2707236*y^5 + 1022210*y^4 - 232680*y^3 + 13080*y^2 + 7938*y - 5250*y^15 + 300*y^16 + 43050*y^14 - 6227505*y^9 + 4042780*y^10 + 7485450*y^8 - 219485*y^13 + 778260*y^12 - 2033220*y^11)/(-1 + y)^21.
%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!.
%o (PARI) a(n) = if(n<1, 0, binomial(n + 20, n) - 7*binomial(n + 14, 14) - 21*binomial(n + 10, 10) + 42*binomial(n + 9, 9) + 105*binomial(n + 6, 6) - 140*binomial(n + 5, 5) + 105*binomial(n + 4, 4) - 420*binomial(n + 3, 3) + 35*binomial(n + 2, 2) + 1050*binomial(n + 1, 1) - 1050*binomial(n, 0) + 300*binomial(n - 1, - 1)) \\ _Harry J. Smith_, Jul 01 2009
%Y Column k=7 of A060092.
%Y Cf. A059948, A060090.
%K nonn
%O 0,6
%A _Vladeta Jovovic_, Feb 26 2001
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