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A277541 n-th derivative of the tenth tetration of x (power tower of order 10) x^^10 at x=1.

%I A277541 #17 Feb 16 2025 08:33:37
%S A277541 1,1,2,9,56,480,5094,65534,984808,16992144,330667680,7130797872,
%T A277541 168564160632,4321664793264,119356965323400,3528831476247240,
%U A277541 111173720474673984,3716755785886791168,131414199676568655552,4899052003032070987968,192050612714621129114880
%N A277541 n-th derivative of the tenth tetration of x (power tower of order 10) x^^10 at x=1.
%C A277541 Differs from A033917 first at n=11.
%H A277541 Alois P. Heinz, <a href="/A277541/b277541.txt">Table of n, a(n) for n = 0..400</a>
%H A277541 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H A277541 Wikipedia, <a href="https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation">Knuth's up-arrow notation</a>
%H A277541 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F A277541 E.g.f.: (x+1)^^10.
%p A277541 f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
%p A277541 a:= n-> n!*coeff(series(f(10), x, n+1), x, n):
%p A277541 seq(a(n), n=0..25);
%t A277541 f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];
%t A277541 a[n_] := n!*SeriesCoefficient[f[10], {x, 0, n}];
%t A277541 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, May 30 2018, from Maple *)
%Y A277541 Column k=10 of A277537.
%Y A277541 Cf. A033917, A215703, A295110.
%K A277541 nonn
%O A277541 0,3
%A A277541 _Alois P. Heinz_, Oct 19 2016