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A097718
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Coefficients in asymptotic expansion of functional equation solution.
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0
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1, -1, -1, 2, 21, 54, -605, -8422, -17815, 915470, 13791711, -14182158, -3814159811, -55759417546, 472583147387, 33181980839114, 418144112565969, -10448831982433506, -511822958265199817, -4431070683610565086
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| E.g.f. A(x) satisfies A(x)=exp(x(A(x)-2)).
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REFERENCES
| N. G. de Bruijn, Asymptotic Methods in Analysis, Dover, 1981, p. 24.
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FORMULA
| E.g.f.: -LambertW(-x*exp(-2*x))/x. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 25 2004
a(n)=sum(k=0..n, binomial(n,k)*((k+1)^(n-1)*2^(n-k)*(-1)^(n+k))); [From Vladimir Kruchinin, Jan 31 2012]
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PROG
| (PARI) a(n)=local(A); if(n<0, 0, A=1+O(x); for(k=1, n, A=exp(x*A-2*x)); n!*polcoeff(A, n))
(Maxima) a(n):=sum(binomial(n, k)*((k+1)^(n-1)*2^(n-k)*(-1)^(n+k)), k, 0, n); [From Vladimir Kruchinin, Jan 31 2012]
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CROSSREFS
| Sequence in context: A005484 A042455 A074875 * A180232 A075681 A034520
Adjacent sequences: A097715 A097716 A097717 * A097719 A097720 A097721
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 22 2004
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