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A360939
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E.g.f. satisfies A(x) = exp( 2*x*A(x) / (1-x) ).
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2
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1, 2, 16, 212, 4016, 99952, 3096448, 115063328, 4993598464, 248071645952, 13888585800704, 865481914527232, 59426130052458496, 4458258196636276736, 362864617248019800064, 31848507841521274769408, 2998685833332127139299328, 301504120063370711801724928
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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) = n! * Sum_{k=0..n} 2^k * (k+1)^(k-1) * binomial(n-1,n-k)/k!.
E.g.f.: exp ( -LambertW(-2*x/(1-x)) ).
E.g.f.: -(1-x)/(2*x) * LambertW(-2*x/(1-x)).
a(n) ~ (1 + 2*exp(1))^(n + 1/2) * n^(n-1) / (sqrt(2) * exp(n - 1/2)). - Vaclav Kotesovec, Nov 10 2023
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PROG
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(PARI) a(n) = n!*sum(k=0, n, 2^k*(k+1)^(k-1)*binomial(n-1, n-k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x/(1-x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1-x)/(2*x)*lambertw(-2*x/(1-x))))
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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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