A295110 a(n) = (1/n) times the n-th derivative of the tenth tetration of x (power tower of order 10) x^^10 at x=1.

1, 1, 3, 14, 96, 849, 9362, 123101, 1888016, 33066768, 648254352, 14047013386, 332435753328, 8525497523100, 235255431749816, 6948357529667124, 218632693287458304, 7300788870920480864, 257844842264845841472, 9602530635731056455744, 376083658114082740084224

Offset: 1

Author

Alois P. Heinz, Nov 14 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..407
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Tetration

Crossrefs

Column k=10 of A295028.

Cf. A277541.

Programs

Maple

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> (n-1)!*coeff(series(f(10), x, n+1), x, n):
seq(a(n), n=1..23);

Mathematica

f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];
a[n_] := (n - 1)!*SeriesCoefficient[f[10], {x, 0, n}];
Array[a, 23] (* Jean-François Alcover, May 31 2018, from Maple *)

Formula

a(n) = 1/n * [(d/dx)^n x^^10]_{x=1}.

a(n) = (n-1)! * [x^n] (x+1)^^10.

a(n) = 1/n * A277541(n).