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A094573
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Triangle T(n,k) giving number of (<=2)-covers of an n-set with k blocks.
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2
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1, 1, 1, 3, 1, 1, 12, 20, 7, 1, 39, 169, 186, 59, 3, 1, 120, 1160, 2755, 2243, 661, 55, 1, 363, 7381, 33270, 52060, 33604, 9167, 910, 15, 1, 1092, 45500, 367087, 988750, 1126874, 601262, 151726, 16401, 525, 1, 3279, 276529, 3873786, 17005149
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OFFSET
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0,4
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COMMENTS
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Cover of a set is (<=2)-cover if every element of the set is covered with at most two blocks of the cover.
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LINKS
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FORMULA
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E.g.f.: exp(-x-x^2/2*(exp(y)-1))*(Sum_{n>=0} exp(y*binomial(n+1, 2))*x^n/n!).
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EXAMPLE
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1;
1;
1,3,1;
1,12,20,7;
1,39,169,186,59,3;
1,120,1160,2755,2243,661,55;
...
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MATHEMATICA
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rows = 9; m = rows + 2;
egf = Exp[-x - (x^2/2)*(Exp[y]-1)]*Sum[Exp[y*Binomial[n+1, 2]]*(x^n/n!), {n, 0, m}];
cc = CoefficientList[# + O[x]^m, x]& /@ CoefficientList[egf + O[y]^m, y];
(Range[0, Length[cc]-1]! * cc)[[1 ;; rows]] /. {0, a__} :> {a} // Flatten (* Jean-François Alcover, May 13 2019 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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