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A321974
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Expansion of e.g.f. exp(exp(x)/(1 - x) - 1).
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3
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1, 2, 9, 54, 404, 3598, 37003, 430300, 5571147, 79358032, 1231990840, 20684884234, 373208232229, 7197079035318, 147658793214733, 3210107125516682, 73690798853163884, 1780718798351625094, 45171972342078432287, 1199948465249850848608, 33305064129201851432591, 963911863209583899492324
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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) = Sum_{k=1..n} A000522(k)*binomial(n-1,k-1)*a(n-k).
a(n) ~ exp(-exp(1)/2 - 3/4 + 2*exp(1/2)*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - Vaclav Kotesovec, Dec 19 2018
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MAPLE
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seq(n!*coeff(series(exp(exp(x)/(1 - x) - 1), x=0, 22), x, n), n=0..21); # Paolo P. Lava, Jan 09 2019
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MATHEMATICA
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nmax = 21; CoefficientList[Series[Exp[Exp[x]/(1 - x) - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Floor[Exp[1] k!] Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 21}]
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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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