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A059946
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Number of 5-block bicoverings of an n-set.
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3
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0, 0, 0, 25, 472, 6185, 70700, 759045, 7894992, 80736625, 817897300, 8241325565, 82783813112, 830046591465, 8313655213500, 83215436364085, 832626645756832, 8329096006484705, 83307920631515300, 833180902353754605, 8332418928963358152, 83327847634888960345
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OFFSET
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1,4
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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LINKS
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FORMULA
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a(n) = (1/5!)*(10^n - 5*6^n - 10*4^n + 20*3^n + 30*2^n - 60).
E.g.f. for m-block bicoverings of an n-set is exp(-x-1/2*x^2*(exp(y)-1))*Sum_{i>=0} (x^i/i!)*exp(binomial(i, 2)*y).
G.f.: x^4*(288*x^2-178*x+25) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)*(10*x-1)). - Colin Barker, Jan 11 2013
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MATHEMATICA
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With[{c=(1/5!)}, Table[c(10^n-5 6^n-10 4^n+20 3^n+30 2^n-60), {n, 20}]] (* Harvey P. Dale, Apr 21 2011 *)
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PROG
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(PARI) a(n) = {(1/5!)*(10^n - 5*6^n - 10*4^n + 20*3^n + 30*2^n - 60)} \\ Andrew Howroyd, Jan 29 2020
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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