cp's OEIS Frontend

A215796 Number of distinct values taken by 7th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1.

%I A215796 #26 Mar 06 2019 20:57:21
%S A215796 1,1,2,4,9,20,48,115,283,691,1681,3988,9241,20681,44217,89644
%N A215796 Number of distinct values taken by 7th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1.
%e A215796 a(4) = 4 because the A000108(3) = 5 possible parenthesizations of x^x^x^x lead to 4 different values of the 7th derivative at x=1: (x^(x^(x^x))) -> 26054; ((x^x)^(x^x)), ((x^(x^x))^x) -> 41090; (x^((x^x)^x)) -> 47110; (((x^x)^x)^x) -> 70098.
%p A215796 T:= proc(n) T(n):=`if`(n=1, [x], map(h-> x^h, g(n-1$2))) end:
%p A215796 g:= proc(n, i) option remember; `if`(i=1, [x^n], [seq(seq(
%p A215796       seq(mul(T(i)[w[t]-t+1], t=1..j)*v, v=g(n-i*j, i-1)), w=
%p A215796       combinat[choose]([$1..nops(T(i))+j-1], j)), j=0..n/i)])
%p A215796     end:
%p A215796 f:= proc() local i, l; i, l:= 0, []; proc(n) while n>
%p A215796       nops(l) do i:= i+1; l:= [l[], T(i)[]] od; l[n] end
%p A215796     end():
%p A215796 a:= n-> nops({map(f-> 7!*coeff(series(subs(x=x+1, f), x, 8), x, 7), T(n))[]}):
%p A215796 seq(a(n), n=1..12);
%Y A215796 Column k=7 of A216368.
%Y A215796 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, A215837.
%K A215796 nonn,more
%O A215796 1,3
%A A215796 _Alois P. Heinz_, Aug 24 2012