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A140606 Number of inequivalent expressions involving n operands. 3
1, 6, 68, 1170, 27142, 793002, 27914126, 1150212810, 54326011414, 2894532443154, 171800282010062, 11243812043430330, 804596872359480358, 62506696942427106498, 5239819196582605428254, 471480120474696200252970, 45328694990444455796547766, 4637556923393331549190920306 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Only binary operators +, -, *, / (and with parentheses) are permitted.

Expression (a+b)-c is equivalent to a-c+b and a+b-c but (a+b)-c is different from a-b+c.

Another example is expression (a-b)/(c-d) is equivalent to (b-a)/(d-c).

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

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)

EXAMPLE

When n=2, there are six inequivalent expressions: a+b, a-b, b-a, a*b, a/b, b/a, while another expression such as b+a is equivalent to a+b.

CROSSREFS

Cf. A182173.

Sequence in context: A186669 A258134 A256238 * A014505 A274722 A127184

Adjacent sequences:  A140603 A140604 A140605 * A140607 A140608 A140609

KEYWORD

nonn,nice

AUTHOR

Zhao Hui Du, Jul 07 2008

STATUS

approved

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Last modified November 15 01:39 EST 2018. Contains 317224 sequences. (Running on oeis4.)