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 A182173 Number of inequivalent expressions involving n operands. 3
 2, 10, 94, 1466, 31814, 887650, 30259198, 1218864842, 56644903958, 2983300619410, 175598066553166, 11423394497044154, 813897286250604326, 63030237104398839490, 5271647928235911880222, 473558482553909252128298, 45473767604938843870986422, 4648336478135316689480390770 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Each operand must be used exactly once, and the only allowed operations are addition, subtraction, multiplication, division, and unary minus. Parentheses are permitted. This sequence differs from A140606 by allowing unary minus. LINKS Jingzhe Tang, Table of n, a(n) for n = 1..300 (first 90 terms from David Radcliffe) David Radcliffe, Python script Wikipedia, 24 Game 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) - 2*x, where B(x) = 2*x + exp(C(x)) - 1 - C(x) and C(x) = 2*x + 2*exp(B(x)) - 2*exp(B(x)/2) - B(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 10 inequivalent expressions: a+b, a-b, b-a, -a-b, a*b, -a*b, a/b, -a/b, b/a, -b/a. PROG (PARI) {a(n) = my(A, B=x +x*O(x^n), C=x +x*O(x^n)); for(i=1, n, B = 2*x + exp(C) - 1 - C; C = 2*x + 2*exp(B) - 2*exp(B/2) - B ); A = B + C - 2*x; n!*polcoeff(A, n)} for(n=1, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Aug 12 2018 - After formula by Zhujun Zhang CROSSREFS Cf. A140606. Sequence in context: A231375 A100622 A103436 * A160940 A193290 A193435 Adjacent sequences:  A182170 A182171 A182172 * A182174 A182175 A182176 KEYWORD nonn AUTHOR David Radcliffe, Apr 16 2012 STATUS approved

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Last modified October 21 06:39 EDT 2019. Contains 328292 sequences. (Running on oeis4.)