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A349505
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E.g.f. satisfies: A(x) = (1 + x)^(A(x)^3).
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7
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1, 1, 6, 81, 1668, 46740, 1659102, 71386602, 3611376360, 210083758704, 13817649943440, 1013979735381888, 82134894774767832, 7279520816638839600, 700730732176038359208, 72803537907677356262760, 8120227815636769492383168
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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) = Sum_{k=0..n} (3*k+1)^(k-1) * Stirling1(n,k).
E.g.f. A(x) = Sum_{k>=0} (3*k+1)^(k-1) * (log(1+x))^k / k!.
E.g.f.: (-LambertW(-3*log(1 + x)) / (3*log(1 + x)))^(1/3).
a(n) ~ n^(n-1) / (sqrt(3) * (exp(exp(-1)/3) - 1)^(n - 1/2) * exp(n + exp(-1)/6 - 5/6)). (End)
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MATHEMATICA
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nmax = 20; CoefficientList[Series[(-LambertW[-3*Log[1 + x]]/(3*Log[1 + x]))^(1/3), {x, 0, nmax}], x]*Range[0, nmax]! (* Vaclav Kotesovec, Nov 20 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (3*k+1)^(k-1)*stirling(n, k, 1));
(PARI) N=20; x='x+O('x^N); Vec(serlaplace(sum(k=0, N, (3*k+1)^(k-1)*log(1+x)^k/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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