login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 3
1, 1, 3, 14, 96, 849, 9362, 123101, 1888016, 33066768, 648254352, 14047013386, 332435753328, 8525497523100, 235255431749816, 6948357529667124, 218632693287458304, 7300788870920480864, 257844842264845841472, 9602530635731056455744, 376083658114082740084224 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

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).

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-Fran├žois Alcover, May 31 2018, from Maple *)

CROSSREFS

Column k=10 of A295028.

Cf. A277541.

Sequence in context: A295107 A295108 A295109 * A136461 A276747 A007470

Adjacent sequences:  A295107 A295108 A295109 * A295111 A295112 A295113

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 14 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)