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%I #9 May 31 2018 03:08:51
%S 1,1,3,14,96,849,9362,118061,1706576,27411888,488133552,9504647866,
%T 201394553808,4607546125740,113271179680136,2976610819616004,
%U 83276079152315904,2470817772641667104,77492234876034762432,2561350116102926727744,88984716683633511515904
%N a(n) = (1/n) times the n-th derivative of the seventh tetration of x (power tower of order 7) x^^7 at x=1.
%H Alois P. Heinz, <a href="/A295107/b295107.txt">Table of n, a(n) for n = 1..416</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation">Knuth's up-arrow notation</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F a(n) = 1/n * [(d/dx)^n x^^7]_{x=1}.
%F a(n) = (n-1)! * [x^n] (x+1)^^7.
%F a(n) = 1/n * A277538(n).
%p f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
%p a:= n-> (n-1)!*coeff(series(f(7), x, n+1), x, n):
%p seq(a(n), n=1..23);
%t f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];
%t a[n_] := (n - 1)!*SeriesCoefficient[f[7], {x, 0, n}];
%t Array[a, 23] (* _Jean-François Alcover_, May 31 2018, from Maple *)
%Y Column k=7 of A295028.
%Y Cf. A277538.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Nov 14 2017
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