The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216403 Number of distinct values taken by 10th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1. 2
 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4763, 12452, 32711, 86239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE a(4) = 4 because the A000108(3) = 5 possible parenthesizations of x^x^x^x lead to 4 different values of the 10th derivative at x=1: (x^(x^(x^x))) -> 37616880; ((x^x)^(x^x)), ((x^(x^x))^x) -> 42409440; (x^((x^x)^x)) -> 77899320; (((x^x)^x)^x) -> 66712680. MAPLE # load programs from A215703, then: a:= n-> nops({map(f-> 10!*coeff(series(subs(x=x+1, f),                   x, 11), x, 10), T(n))[]}): seq(a(n), n=1..11); CROSSREFS Cf. A000081 (distinct functions), A000108 (parenthesizations), A000012 (first derivatives), A028310 (2nd derivatives), A199085 (3rd derivatives), A199205 (4th derivatives), A199296 (5th derivatives), A199883 (6th derivatives), A002845, A003018, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A082499, A196244, A198683, A215703, A215840. Column k=10 of A216368. Sequence in context: A318803 A318856 A255640 * A145548 A292555 A318804 Adjacent sequences:  A216400 A216401 A216402 * A216404 A216405 A216406 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 06 2012 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.

Last modified September 23 21:27 EDT 2020. Contains 337315 sequences. (Running on oeis4.)