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A075887 a(n) = 1 + n + n[n/2] + n[n/2][n/3] +... + n[n/2][n/3]...[n/n], where [x]=ceiling(x).

%I A075887 #19 Sep 08 2022 08:45:07
%S A075887 1,2,5,16,45,171,421,1968,4553,19225,57261,226854,496309,3136420,
%T A075887 6764563,24850336,84877201,380461599,805949533,4411165990,9288196621,
%U A075887 48275465722,154143694937,527401107276,1100708161081,8151403215501
%N A075887 a(n) = 1 + n + n[n/2] + n[n/2][n/3] +... + n[n/2][n/3]...[n/n], where [x]=ceiling(x).
%C A075887 a(n) ~ L^n where L = 3.517487255902369649399793699323864170685620..., with log(L) = Sum_{k=1..inf} log(k+1)/(k*(k+1)) = 1.2577468869443696300... (cf. A131688).
%H A075887 Paul D. Hanna, <a href="/A075887/b075887.txt">Table of n, a(n) for n = 0..1000</a>
%F A075887 a(n) = 1 + Sum_{m=1..n} Product_{k=1..m} ceiling(n/k) for n>0 and a(0)=1.
%e A075887 a(5) = 171 = 1 +5[5/2] +5[5/2][5/3] +5[5/2][5/3][5/4] +5[5/2][5/3][5/4][5/5] = 1 + 5 + 5*3 + 5*3*2 + 5*3*2*2 + 5*3*2*2*1, here [x]=ceiling(x).
%t A075887 Table[1 +Sum[Product[Ceiling[n/k], {k,1,j}], {j,1,n}], {n,0,50}] (* _G. C. Greubel_, Oct 11 2018 *)
%o A075887 (PARI) {a(n) = 1 + sum(m=1,n,prod(k=1,m,ceil(n/k)))}
%o A075887 for(n=0,40,print1(a(n),", "))
%o A075887 (Magma) [1] cat [1 + (&+[(&*[Ceiling(n/k): k in [1..j]]): j in [1..n]]): n in [1..50]]; // _G. C. Greubel_, Oct 11 2018
%Y A075887 Cf. A131385, A131688.
%K A075887 easy,nonn
%O A075887 0,2
%A A075887 _Paul D. Hanna_, Oct 17 2002