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A217906
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O.g.f.: 1 / Sum_{n>=0} -n^n*(n-1)^(n-1) * exp(-n*(n-1)*x) * x^n / n!.
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2
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1, 1, 3, 19, 223, 4019, 98071, 3012595, 111408735, 4813926235, 237893755847, 13230156372931, 817650834368367, 55588558619887179, 4122802071853330711, 331247290236326404499, 28660436738240190615167, 2656810905539387715877787, 262694577305483845458361767
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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) ~ 2^(2*n - 2) * n^(n - 3/2) / (sqrt(Pi) * sqrt(1-c) * exp(n) * c^(n - 1/2) * (2-c)^(n-1)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - Vaclav Kotesovec, Aug 22 2018
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EXAMPLE
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O.g.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 223*x^4 + 4019*x^5 + 98071*x^6 +...
where
A(x) = 1/(1 - 1^1*0^0*x*exp(-1*0*x) - 2^2*1^1*exp(-2*1*x)*x^2/2! - 3^3*2^2*exp(-3*2*x)*x^3/3! - 4^4*3^3*exp(-4*3*x)*x^4/4! - 5^5*4^4*exp(-5*4*x)*x^5/5! +...).
simplifies to a power series in x with integer coefficients.
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PROG
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(PARI) {a(n)=polcoeff(1/sum(m=0, n, -m^m*(m-1)^(m-1)*x^m*exp(-m*(m-1)*x+x*O(x^n))/m!), n)}
for(n=0, 30, print1(a(n), ", "))
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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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