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A370894
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Expansion of e.g.f. (1/x) * Series_Reversion( x*(3 - exp(2*x))/2 ).
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2
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1, 1, 6, 64, 1016, 21576, 575680, 18525088, 698625408, 30229271680, 1476535180544, 80371762466304, 4824793854177280, 316685993746640896, 22563822118152880128, 1734427247284290015232, 143072322233503079038976, 12606854482934004152303616
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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) = (1/(n+1)!) * Sum_{k=0..n} 2^(n-k) * (n+k)! * Stirling2(n,k).
a(n) ~ 2^(2*n+1) * LambertW(3*exp(1))^(n+1) * n^(n-1) / (sqrt(1 + LambertW(3*exp(1))) * 3^(n+1) * exp(n) * (LambertW(3*exp(1)) - 1)^(2*n+1)). - Vaclav Kotesovec, Mar 06 2024
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(3-exp(2*x))/2)/x))
(PARI) a(n) = sum(k=0, n, 2^(n-k)*(n+k)!*stirling(n, k, 2))/(n+1)!;
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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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