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A295105
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a(n) = (1/n) times the n-th derivative of the fifth tetration of x (power tower of order 5) x^^5 at x=1.
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3
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1, 1, 3, 14, 96, 729, 6842, 71861, 869936, 11639208, 172823592, 2797075786, 49197117648, 931938081060, 18931744650296, 410210251648404, 9443418462484224, 230108297407058144, 5915598580747789632, 159987606074180375904, 4539874767394840811904
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = 1/n * [(d/dx)^n x^^5]_{x=1}.
a(n) = (n-1)! * [x^n] (x+1)^^5.
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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(5), 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[5], {x, 0, n}];
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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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