cp's OEIS Frontend

A306679 a(n) = round(1/(1-Integral_{x=0..1} f_n(x) dx)), where f_n is the n-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways.

%I A306679 #22 Sep 13 2019 21:41:41
%S A306679 2,5,10,2,17,6,2,4,26,13,3,5,8,2,2,4,2,37,21,8,11,15,3,5,5,6,9,6,2,2,
%T A306679 3,2,2,4,4,2,3,50,32,16,3,19,23,7,11,2,4,7,10,12,16,13,2,3,6,3,5,5,7,
%U A306679 6,5,9,8,6,8,2,2,2,2,2,4,2,2,2,2,2,5,4,3,4,4
%N A306679 a(n) = round(1/(1-Integral_{x=0..1} f_n(x) dx)), where f_n is the n-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways.
%C A306679 The ordering of the functions f_n is defined in A215703: f_1, f_2, ... = x, x^x, x^(x^2), x^(x^x), x^(x^3), x^(x^x*x), x^(x^(x^2)), x^(x^(x^x)), x^(x^4), x^(x^x*x^2), ... . Values of new records are in A322008.
%H A306679 Alois P. Heinz, <a href="/A306679/b306679.txt">Table of n, a(n) for n = 1..20299</a>
%F A306679 a(n) >= 2 for n >= 1.
%p A306679 T:= proc(n) T(n):=`if`(n=1, [x], map(h-> x^h, g(n-1$2))) end:
%p A306679 g:= proc(n, i) option remember; `if`(i=1, [x^n], [seq(seq(
%p A306679       seq(mul(T(i)[w[t]-t+1], t=1..j)*v, v=g(n-i*j, i-1)), w=
%p A306679       combinat[choose]([$1..nops(T(i))+j-1], j)), j=0..n/i)])
%p A306679     end:
%p A306679 a:= proc() local i, l; i, l:= 0, []; proc(n) while n>
%p A306679       nops(l) do i:= i+1; l:= [l[], map(f-> round(evalf(
%p A306679       1/(1-int(f, x=0..1)))), T(i))[]] od; l[n] end
%p A306679     end():
%p A306679 seq(a(n), n=1..100);
%Y A306679 Cf. A000081, A087803, A215703, A322008.
%K A306679 nonn,look
%O A306679 1,1
%A A306679 _Alois P. Heinz_, Mar 04 2019