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A166895
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a(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k), n>=1.
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8
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1, 3, 7, 39, 366, 5697, 194881, 16288695, 2430565261, 564615230758, 257227244037248, 319346787227133873, 832952161388710135215, 3382434539389226013260403, 22966972221673234523620345857
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 39*x^4/4 + 366*x^5/5 + 5697*x^6/6 +...
exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 14*x^4 + 89*x^5 + 1050*x^6 +...+ A166894(n)*x^n +...
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MATHEMATICA
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Table[Sum[Binomial[n - k, k]^(n - k) *n/(n - k), {k, 0, Floor[n/2]}], {n, 1, 25}] (* G. C. Greubel, May 27 2016 *)
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PROG
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(PARI) a(n)=sum(k=0, n\2, binomial(n-k, k)^(n-k)*n/(n-k))
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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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