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A222146
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a(n) = n-th third-order hyperharmonic-exponential number, multiplied by n!.
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0
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0, 1, 9, 116, 2082, 49774, 1525752, 58180632, 2694333744, 148623965136, 9611353576800, 719080605842400, 61545135592056960, 5968396255982428800, 650359540100397012480, 79053322881277342886400, 10650510963204404347238400, 1581353364394671905218406400
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (Sum_{k=0..n} A008277(n,k) * H3(k)) * A000142(n) where H3(k) is defined by g.f.: - log(1-x)/(1-x)^3. - Michel Marcus, Feb 09 2013
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PROG
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(PARI)
hyp(n, alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y); }
a(n, alpha=3) = sum(k=0, n, n!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k, alpha));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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