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A366252
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Number of convergent binary relations on [n] (A365534) that converge to a quasi-order relation (A000798).
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2
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OFFSET
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0,3
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COMMENTS
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Equivalently, a(n) is the number of convergent Boolean relation matrices whose Frobenius normal form is such that all the diagonal blocks are primitive (A070322).
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LINKS
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FORMULA
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Sum_{n>=0} a_n*x^n/(2^n*binomial(n,2)) = 1/(E(x) @ exp(-(p(x)-1))) where E(x) = Sum_{n>=0} x^n/(2^n*binomial(n,2)), p(x) is the e.g.f. for A070322, and @ is the exponential Hadamard product (see Panafieu and Dovgal).
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MATHEMATICA
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nn = 6; B[n_] := 2^Binomial[n, 2] n!; pr[x_] := Total[primitive Table[x^i/i!, {i, 0, 6}]]; ggf[egf_] := Normal[Series[egf, {x, 0, nn}]] /.
Table[x^i ->x^i/2^Binomial[i, 2], {i, 0, nn}]; Table[B[n], {n, 0, nn}] CoefficientList[Series[1/ggf[Exp[- (pr[x] - 1)]], {x, 0, nn}], x]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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