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 A085466 a(n) is the denominator of the polynomial in e^2 giving the (2n)th du Bois Reymond constant. 8
 2, 8, 32, 384, 1536, 10240, 368640, 10321920, 4587520, 297271296, 29727129600, 435997900800, 15695924428800, 116598295756800, 1523551064555520, 1371195958099968000, 5484783832399872000, 41440588955910144000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..18. Eric Weisstein's World of Mathematics, du Bois-Reymond Constants. EXAMPLE {(-7 + e^2)/2, (-25 - 4*e^2 + e^4)/8, (-98 + 3*e^2 - 6*e^4 + e^6)/32} 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 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 *) CROSSREFS Cf. A085467. Cf. A062545, A062546, A085466, A085467, A138729, A138730, A138731, A138732, A138733. Sequence in context: A134751 A139014 A063505 * A084039 A135620 A134708 Adjacent sequences: A085463 A085464 A085465 * A085467 A085468 A085469 KEYWORD nonn AUTHOR Eric W. Weisstein, Jul 01 2003 EXTENSIONS More terms from R. J. Mathar, Apr 05 2007 Extended by Max Alekseyev, Sep 15 2009 STATUS approved

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Last modified August 10 03:37 EDT 2024. Contains 375044 sequences. (Running on oeis4.)