A277540 n-th derivative of the ninth tetration of x (power tower of order 9) x^^9 at x=1.

1, 1, 2, 9, 56, 480, 5094, 65534, 984808, 16992144, 327038880, 6951172272, 160900135032, 4030551570864, 108477114581640, 3122444423175240, 95686679702270784, 3110711057099693568, 106921473349790826432, 3874480434910990168128, 147622208056015906586880

Offset: 0

Author

Alois P. Heinz, Oct 19 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Tetration

Crossrefs

Column k=9 of A277537.

Cf. A215703, A295109.

Programs

Maple

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> n!*coeff(series(f(9), x, n+1), x, n):
seq(a(n), n=0..25);

Mathematica

f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];
a[n_] := n!*SeriesCoefficient[f[9], {x, 0, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Formula

E.g.f.: (x+1)^^9.