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A274269
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a(n) = (5*n - 1)^(n-1).
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5
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1, 9, 196, 6859, 331776, 20511149, 1544804416, 137231006679, 14048223625216, 1628413597910449, 210832519264920576, 30155888444737842659, 4722366482869645213696, 803596764671634487466709, 147653612273582215982104576, 29134419507545592909032289199
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f. A(x) = 1 - exp(-1/5*T(5*x)) = x + 9*x^2/2! + 14^2*x^3/3! + 19^3*x^4/4! + 24^4*x^5/5! + ..., where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
A(x) = series reversion( (1 - x)^5*log(1/(1 - x)) ). See A274270.
1 - A(x) = exp(-x/(1 - A(x))^5) = exp(-x/(exp(-5*x/(exp(-5*x/ ...))))).
1 - A(-x*exp(5*x)) = exp(x) = 1/(1 - A(x*exp(-5*x))).
1/(1 - A(x)) = Sum_{n >= 0} (5*n + 1)^(n-1)*x^n/n!, the e.g.f. for A052782.
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MAPLE
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MATHEMATICA
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Table[(5*n-1)^(n-1), {n, 1, 25}] (* G. C. Greubel, Jun 19 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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