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A295104
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a(n) = (1/n) times the n-th derivative of the fourth tetration of x (power tower of order 4) x^^4 at x=1.
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3
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1, 1, 3, 14, 72, 489, 3722, 33641, 334520, 3761688, 45898272, 615641806, 8863726704, 137786878644, 2279658872696, 40229212948404, 750433323448128, 14801457167223872, 306869893647304896, 6683254543551623904, 152281219079726183040, 3626445842114839589952
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OFFSET
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1,3
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COMMENTS
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First term < 0: a(329).
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LINKS
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FORMULA
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a(n) = 1/n * [(d/dx)^n x^^4]_{x=1}.
a(n) = (n-1)! * [x^n] (x+1)^^4.
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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(4), 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[4], {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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