A085466 a(n) is the denominator of the polynomial in e^2 giving the (2n)th du Bois Reymond constant.
2, 8, 32, 384, 1536, 10240, 368640, 10321920, 4587520, 297271296, 29727129600, 435997900800, 15695924428800, 116598295756800, 1523551064555520, 1371195958099968000, 5484783832399872000, 41440588955910144000
Offset: 1
Keywords
Examples
{(-7 + e^2)/2, (-25 - 4*e^2 + e^4)/8, (-98 + 3*e^2 - 6*e^4 + e^6)/32}
Links
- Eric Weisstein's World of Mathematics, du Bois-Reymond Constants.
Crossrefs
Programs
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Maple
a := proc(n) local r ; r := residue(x^2/(1+x^2)^n/(tan(x)-x),x=I) ; r := -3-2*subs(tanh(1)=(x-1/x)/(x+1/x),%) ; r := taylor(r,x=0,16*n+2) ; cf := 1 ; for p from 0 to 2*n by 2 do cf := lcm(cf,denom(coeftayl(r,x=0,p))) ; od ; r := simplify(convert(r*cf,polynom)) ; RETURN([cf,r]) ; end: A085466 := proc() # n = 1 invalid formula printf("2, ") ; for n from 2 to 14 do a085467 := a(n)[1] : printf("%d, ",a085467) ; od : end: A085466() ; # R. J. Mathar, Apr 05 2007
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Mathematica
a = {}; Do[p = FullSimplify[TrigToExp[ -3 - 2Residue[x^2/((Tan[x] - x) (1 + x^2)^n), {x, I}]]]; AppendTo[a, Denominator[p]], {n, 1, 9}]; a (* Artur Jasinski, Mar 26 2008 *)
Extensions
More terms from R. J. Mathar, Apr 05 2007
Extended by Max Alekseyev, Sep 15 2009