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A355111
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Expansion of e.g.f. 3 / (4 - 3*x - exp(3*x)).
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6
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1, 2, 11, 93, 1041, 14541, 243747, 4767183, 106556373, 2679469065, 74864397015, 2300883358995, 77144051804409, 2802027511061325, 109604157405491691, 4593512301562215783, 205348466229473678301, 9753645833118762303249, 490530576727430107027839, 26040317900991310393061499
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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(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} binomial(n,k) * 3^(k-1) * a(n-k).
a(n) ~ n! / ((1 + LambertW(exp(4))) * ((4 - LambertW(exp(4)))/3)^(n+1)). - Vaclav Kotesovec, Jun 19 2022
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MATHEMATICA
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nmax = 19; CoefficientList[Series[3/(4 - 3 x - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 3^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
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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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