A277539 - OEIS

%I #14 May 30 2018 03:29:18

%S 1,1,2,9,56,480,5094,65534,984808,16629264,312523680,6425601072,

%T 143775827832,3471659156784,90060216241800,2496918043296840,

%U 73703868906725184,2307477802376274048,76376765284713220032,2664806795257276548288,97747916619062963335680

%N n-th derivative of the eighth tetration of x (power tower of order 8) x^^8 at x=1.

%H Alois P. Heinz, <a href="/A277539/b277539.txt">Table of n, a(n) for n = 0..400</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 E.g.f.: (x+1)^^8.

%p f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:

%p a:= n-> n!*coeff(series(f(8), x, n+1), x, n):

%p seq(a(n), n=0..25);

%t f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];

%t a[n_] := n!*SeriesCoefficient[f[8], {x, 0, n}];

%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, May 30 2018, from Maple *)

%Y Column k=8 of A277537.

%Y Cf. A215703, A295108.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Oct 19 2016