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A357246
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E.g.f. satisfies A(x) * log(A(x)) = (1-x) * (exp(x) - 1).
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1
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1, 1, -2, 5, -49, 497, -6926, 116510, -2325422, 53538315, -1397740279, 40792008435, -1316056239994, 46509292766172, -1786748828967402, 74139054468535061, -3304409577659864305, 157444695280699565069, -7986085592316390890618, 429645521271113815480246
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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.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * ((1-x) * (exp(x) - 1))^k / k!.
E.g.f.: A(x) = exp( LambertW((1-x) * (exp(x) - 1)) ).
E.g.f.: A(x) = (1-x) * (exp(x) - 1)/LambertW((1-x) * (exp(x) - 1)).
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MATHEMATICA
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nmax = 19; A[_] = 1;
Do[A[x_] = Exp[-(((Exp[x]-1)*(x-1))/A[x])]+O[x]^(nmax+1)//Normal, {nmax}];
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k+1)^(k-1)*((1-x)*(exp(x)-1))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw((1-x)*(exp(x)-1)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1-x)*(exp(x)-1)/lambertw((1-x)*(exp(x)-1))))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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