A277538 n-th derivative of the seventh tetration of x (power tower of order 7) x^^7 at x=1.

1, 1, 2, 9, 56, 480, 5094, 65534, 944488, 15359184, 274118880, 5369469072, 114055774392, 2618129199504, 64505645760360, 1699067695202040, 47625773113856064, 1415693345589370368, 44474719907550007872, 1472352462644660486208, 51227002322058534554880

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=7 of A277537.

Cf. A215703, A295107.

Programs

Maple

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> n!*coeff(series(f(7), x, n+1), x, n):
seq(a(n), n=0..25);

Mathematica

f[0] = 1; f[n_] := f[n] = (x + 1)^f[n - 1];
a[n_] := n! SeriesCoefficient[f[7], {x, 0, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 29 2018, from Maple *)

Formula

E.g.f.: (x+1)^^7.