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A295103
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a(n) = (1/n) times the n-th derivative of the third tetration of x (power tower of order 3) x^^3 at x=1.
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3
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1, 1, 3, 8, 36, 159, 932, 5627, 40016, 302364, 2510712, 22623490, 213486864, 2227719948, 23388469400, 277570328040, 3182959484736, 42530335589088, 523078873327872, 7846745537655360, 101370634558327680, 1717052148685665792, 22657314273376353408
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OFFSET
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1,3
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COMMENTS
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First term < 0: a(33) = -26329560314038014690778779463680.
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LINKS
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FORMULA
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a(n) = 1/n * [(d/dx)^n x^^3]_{x=1}.
a(n) = (n-1)! * [x^n] (x+1)^^3.
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MAPLE
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f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> (n-1)!*coeff(series(f(3), x, n+1), x, n):
seq(a(n), n=1..23);
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MATHEMATICA
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f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];
a[n_] := (n - 1)!*SeriesCoefficient[f[3], {x, 0, n}];
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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