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A355247
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Expansion of e.g.f. exp(2*(exp(x) - 1 + x)).
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4
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1, 4, 18, 90, 494, 2946, 18926, 130066, 950654, 7353794, 59954638, 513333618, 4601380766, 43062556322, 419742815726, 4252083713874, 44680229906622, 486145710591874, 5468499473222670, 63503107472489266, 760281866742088670, 9373065303624742498, 118858898763010225198
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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^(n+2) * exp(n/LambertW(n/2) - n - 2) / (4 * sqrt(1 + LambertW(n/2)) * LambertW(n/2)^(n+2)).
a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k+1) * Bell(n-k+1). - Ilya Gutkovskiy, Jun 26 2022
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MATHEMATICA
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nmax = 25; CoefficientList[Series[Exp[2*Exp[x]-2+2*x], {x, 0, nmax}], x] * Range[0, nmax]!
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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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