A140606 Number of inequivalent expressions involving n operands.
1, 6, 68, 1170, 27142, 793002, 27914126, 1150212810, 54326011414, 2894532443154, 171800282010062, 11243812043430330, 804596872359480358, 62506696942427106498, 5239819196582605428254, 471480120474696200252970, 45328694990444455796547766, 4637556923393331549190920306
Offset: 1
Examples
When n=2, there are six inequivalent expressions: a+b, a-b, b-a, a*b, a/b, b/a. Other expressions are equivalent to these (e.g. b+a is equivalent to a+b).
Links
- Jingzhe Tang, Table of n, a(n) for n = 1..300
- Author?, A Chinese web page containing the first 100 terms and C source code to generate it
- Author?, A Chinese web page where the problem originated
- Ruud H.G. van Tol, Perl port of the C source code
- Zhujun Zhang, A Chinese web page on exponential generating function
- Zhujun Zhang, A Chinese web page on approximation
Formula
From Zhujun Zhang, Aug 11 2018: (Start)
E.g.f.: A(x) = B(x)+C(x)-D(x)-E(x)-x, where B(x) = 2x+exp(C(x))-1-C(x), C(x) = 2x+2*exp(B(x))-2*exp(B(x)/2)-B(x), D(x) = x+exp(E(x))-1-E(x), and E(x) = x+exp(2*D(x))-exp(D(x))-D(x).
a(n) ~ (n/(e*b))^n * sqrt(b)*c/n, where b=0.16142418303980816579438744831086877555003744810690... and c=1.8772213095052105788245813534431275116981368728916.... (End)
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