This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A216403 #6 Oct 04 2014 10:53:12
%S A216403 1,1,2,4,9,20,48,115,286,719,1842,4763,12452,32711,86239
%N 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.
%e A216403 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.
%p A216403 # load programs from A215703, then:
%p A216403 a:= n-> nops({map(f-> 10!*coeff(series(subs(x=x+1, f),
%p A216403 x, 11), x, 10), T(n))[]}):
%p A216403 seq(a(n), n=1..11);
%Y A216403 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.
%K A216403 nonn
%O A216403 1,3
%A A216403 _Alois P. Heinz_, Sep 06 2012