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 A169608 a(n) is the number of ways to evaluate a polynomial of degree n, say p0 + p1*x + ... + pn*x^n, where each addition or multiplication takes exactly two arguments. 2
 1, 1, 7, 163, 11602, 2334244, 1304066578, 1972869433837, 8012682343669366, 86298937651093314877, 2449381767217281163362301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Guillaume Revy, Implementation of binary floating-point arithmetic on embedded integer processors, Ph D Thesis, University Lyon - ENS Lyon, December 2009, Table 6.1 in Section 6.1.6 LINKS EXAMPLE For example, there are 7 ways to evaluate a polynomial of degree 2: ((a0+(x*a1))+(x*(x*a2))) ((a0+(x*a1))+((x*x)*a2)) (a0+(x*(a1+(x*a2)))) (a0+((x*a1)+(x*(x*a2)))) (a0+((x*a1)+((x*x)*a2))) ((x*a1)+(a0+(x*(x*a2)))) ((x*a1)+(a0+((x*x)*a2))) MAPLE cparen := proc(e) local i, l, s, a, b, pa, pb, la, ee, e1, v, t, g; option remember; if type(e, name) then 1 elif type(e, `+`) then s := 0; ee := convert(e, list); e1 := ee[1]; ee := subsop(1=NULL, ee); for i from 0 to nops(ee)-1 do for la in combinat[choose](ee, i) do a := e1+convert(la, `+`); b := e-a; pa := procname(a); pb := procname(b); s := s + pa * pb; od od; g := 0; for a in e while g<>1 do g:=gcd(g, a) od; if g=1 then g:=[] elif type(g, `*`) then g:=convert(g, list) else g:=[g] fi; g := map(proc(t) if type(t, `^`) then op(1, t)\$op(2, t) else t fi end, g); for i from 1 to nops(g) do for v in combinat[choose](g, i) do a := convert(v, `*`); t := expand(e/a); s := s + procname(a)*procname(t); od od; s elif type(e, `*`) or type(e, `^`) then s := 0; if type(e, `*`) then ee := convert(e, list) else ee:=[e] fi; ee := map(proc(t) if type(t, `^`) then op(1, t)\$op(2, t) else t fi end, ee); for i from 1 to iquo(nops(ee), 2) do for la in combinat[choose](ee, i) do a := convert(la, `*`); b := e/a; if 2*i=nops(ee) and op(1, {a, b})<>a then next fi; if a=b then s := s + (procname(a) * (1+procname(a))) / 2; else s := s + procname(a)*procname(b); fi od od; s else ERROR("unexpected type", whattype(e), e) fi end: A169608 := proc(n) cparen(sum(p[i] * x^i, i=0..n)); end: CROSSREFS Sequence in context: A027549 A212856 A351610 * A184754 A160241 A020998 Adjacent sequences: A169605 A169606 A169607 * A169609 A169610 A169611 KEYWORD nice,nonn AUTHOR Christophe Mouilleron, Dec 03 2009, Jan 23 2010 EXTENSIONS Author's name changed by N. J. A. Sloane, Dec 17 2009, at the request of Paul Zimmermann Minor editing of definition by N. J. A. Sloane, Dec 19 2009 Add a(7) to a(10) Christophe Mouilleron, Jan 04 2010 STATUS approved

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Last modified December 2 11:02 EST 2022. Contains 358493 sequences. (Running on oeis4.)