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A052782
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a(n) = (5*n+1)^(n-1).
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5
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1, 1, 11, 256, 9261, 456976, 28629151, 2176782336, 194754273881, 20047612231936, 2334165173090451, 303305489096114176, 43513917611435838661, 6831675453247426400256, 1165087474585497590531111, 214481724045177216015794176, 42391158275216203514294433201
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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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E.g.f.: exp(-1/5*LambertW(-5*x)).
The e.g.f. A(x) = 1 + x + 11*x^2/2! + 256*x^3/3! + 9261*x^4/4! + ... satisfies:
1) A(x*exp(-5*x)) = exp(x) = 1/A(-x*exp(5*x));
2) A^5(x) = 1/x*series reversion(x*exp(-5*x));
3) A(x^5) = 1/x*series reversion(x*exp(-x^5));
4) A(x) = exp(x*A(x)^5);
5) A(x) = 1/A(-x*A(x)^10). (End)
Related to A001721 by Sum_{n >= 1} a(n)*x^n/n! = series reversion( 1/(1 + x)^5*log(1 + x) ) = series reversion(x - 11*x^2/2! + 107*x^3/3! - 1066*x^4/4! + ...). Cf. A000272, A052750. - Peter Bala, Jun 15 2016
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MAPLE
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spec := [S, {S=Set(B), B=Prod(Z, S, S, S, S, S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nmax = 50}, CoefficientList[Series[Exp[-LambertW[-5*x]/5], {x, 0, nmax}], x]*Range[0, nmax]!] (* or *) Table[(5*n+1)^(n-1), {n, 0, 50}] (* G. C. Greubel, Nov 16 2017 *)
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PROG
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(PARI) for(n=0, 50, print1((5*n+1)^(n-1), ", ")) \\ G. C. Greubel, Nov 16 2017
(PARI) x='x+O('x^50); Vec(serlaplace(exp(-lambertw(-5*x)/5))) \\ G. C. Greubel, Nov 16 2017
(Magma) [(5*n+1)^(n-1): n in [0..50]]; // G. C. Greubel, Nov 16 2017
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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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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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