cp's OEIS Frontend

A199883 Number of distinct values taken by 6th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1.

%I A199883 #15 Sep 26 2014 16:34:56
%S A199883 1,1,2,4,9,20,48,113,262,591,1263,2505,4764,8479,14285,22871,35316,
%T A199883 52755,76517,107826,148914,202715,270622
%N A199883 Number of distinct values taken by 6th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1.
%e A199883 a(4) = 4 because the A000108(3) = 5 possible parenthesizations of x^x^x^x lead to 4 different values of the 6th derivative at x=1: (x^(x^(x^x))) -> 2934; ((x^x)^(x^x)), ((x^(x^x))^x) -> 4908; (x^((x^x)^x)) -> 5034; (((x^x)^x)^x) -> 8322.
%p A199883 f:= proc(n) option remember;
%p A199883       `if`(n=1, {[0, 0, 0, 0, 0]},
%p A199883                 {seq(seq(seq([2+g[1], 3*(1 +g[1] +h[1]) +g[2],
%p A199883                  8 +12*g[1] +6*h[1]*(1+g[1]) +4*(g[2]+h[2])+g[3],
%p A199883                  10+50*h[1]+10*h[2]+5*h[3]+(30+30*h[1]+10*h[2]
%p A199883                  +15*g[1])*g[1]+(20+10*h[1])*g[2]+5*g[3]+g[4],
%p A199883                  45*h[1]*g[1]^2+(120+60*h[2]+15*h[3]+60*g[2]+
%p A199883                  270*h[1])*g[1]+54+15*h[3]+30*g[3]+6*g[4]+
%p A199883                  60*h[1]*g[2]+15*h[1]*g[3]+30*h[1]+ 20*h[2]*g[2]+
%p A199883                  100*h[2]+90*h[1]^2+g[5]+60*g[2]+6*h[4]],
%p A199883                  h=f(n-j)), g=f(j)), j=1..n-1)})
%p A199883     end:
%p A199883 a:= n-> nops(map(x-> x[5], f(n))):
%p A199883 seq(a(n), n=1..15);
%Y A199883 Cf. A000081 (distinct functions), A000108 (parenthesizations), A000012 (first derivatives), A028310 (2nd derivatives), A199085 (3rd derivatives), A199205 (4th derivatives), A199296 (5th derivatives), A002845, A003018, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A082499, A196244, A198683, A215703, A215836. Column k=6 of A216368.
%K A199883 nonn,more
%O A199883 1,3
%A A199883 _Alois P. Heinz_, Nov 11 2011
%E A199883 a(22)-a(23) from _Alois P. Heinz_, Sep 26 2014