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A356908
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E.g.f. satisfies A(x)^A(x) = 1/(1 - x)^2.
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4
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1, 2, -2, 24, -272, 4840, -107496, 2934400, -94501760, 3511914624, -147882696960, 6959217277056, -361941871760256, 20616017227643136, -1276341094954066176, 85337532623368181760, -6128269375791673718784, 470426144496265208979456
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} 2^k * (-k+1)^(k-1) * |Stirling1(n,k)|.
E.g.f.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * (-2 * log(1-x))^k / k!.
E.g.f.: A(x) = exp( LambertW(-2 * log(1-x)) ).
E.g.f.: A(x) = -2 * log(1-x)/LambertW(-2 * log(1-x)).
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MAPLE
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S:= series(exp( LambertW(-2 * log(1-x))), x, 51):
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MATHEMATICA
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nmax = 20; A[_] = 1;
Do[A[x_] = (1/(1-x)^2)^(1/A[x]) + O[x]^(nmax+1) // Normal, {nmax}];
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PROG
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(PARI) a(n) = sum(k=0, n, 2^k*(-k+1)^(k-1)*abs(stirling(n, k, 1)));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k+1)^(k-1)*(-2*log(1-x))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(-2*log(1-x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-2*log(1-x)/lambertw(-2*log(1-x))))
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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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