A277529 Decimal expansion of the eighth derivative of the infinite power tower function x^x^x... at x = 1/2, negated.

5, 0, 1, 0, 9, 2, 7, 6, 2, 7, 5, 0, 3, 6, 6, 9, 6, 8, 9, 5, 8, 6, 8, 0, 1, 7, 2, 3, 5, 3, 2, 2, 9, 4, 5, 1, 2, 7, 2, 1, 8, 3, 9, 4, 2, 3, 8, 3, 2, 4, 2, 6, 2, 4, 4, 6, 0, 2, 8, 9, 9, 9, 1, 1, 8, 5, 8, 4, 6, 3, 2, 4, 1, 1, 0, 1, 8, 9, 6, 2, 0, 2, 8, 2, 1, 0, 6, 6, 7, 3, 8, 4, 1, 4, 3, 1, 6, 6, 8, 7, 3, 6, 1, 0, 8, 7

Offset: 5

Author

Alois P. Heinz, Oct 19 2016

Keywords

• nonn
• cons

Examples

			-50109.2762750366968958680172353229451272183942...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1004
• Eric Weisstein's World of Mathematics, Power Tower.
• Wikipedia, Tetration.

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277527, A277528, A277530, A277531.

Programs

Mathematica

f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[8][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)