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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 September 25 12:38 EDT 2021. Contains 347654 sequences. (Running on oeis4.)