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A215691
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n-th derivative of (x^x)^(x^(x^x)) at x=1.
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3
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1, 1, 4, 18, 124, 950, 8688, 89600, 1038392, 13309272, 186471480, 2837173152, 46466835072, 815532508440, 15246845864040, 302533865599800, 6344720827608384, 140208886623418752, 3254819745378435264, 79172189409906466560, 2013138139856523598080
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OFFSET
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0,3
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COMMENTS
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Also n-th derivative of (x^(x^(x^x)))^x = x^(x^(x^x)*x) at x=1.
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LINKS
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FORMULA
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E.g.f.: (x+1)^((x+1)^((x+1)^(x+1)+1)).
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MAPLE
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a:= n-> n!*coeff(series(subs(x=x+1, (x^x)^(x^(x^x))), x, n+1), x, n):
seq(a(n), n=0..30);
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MATHEMATICA
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m = 20;
CoefficientList[(x+1)^((x+1)^((x+1)^(x+1)+1)) + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, Feb 07 2021 *)
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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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