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Search: id:A085466
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| A085466 |
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a(n) is the denominator of the polynomial in e^2 giving the (2n)th du Bois Reymond constant. |
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+0
8
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| 2, 8, 32, 384, 1536, 10240, 368640, 10321920, 4587520, 297271296, 29727129600, 435997900800, 15695924428800, 116598295756800, 1523551064555520, 1371195958099968000, 5484783832399872000, 41440588955910144000
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Du Bois Reymond Constants
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EXAMPLE
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{(-7 + e^2)/2, (-25 - 4*e^2 + e^4)/8, (-98 + 3*e^2 - 6*e^4 + e^6)/32}
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Apr 05 2007
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MATHEMATICA
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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 (grafix(AT)csl.pl), Mar 26 2008
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CROSSREFS
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Cf. A085467.
Cf. A062545, A062546, A085466, A085467, A138729, A138730, A138731, A138732, A138733.
Sequence in context: A134751 A139014 A063505 this_sequence A084039 A135620 A134708
Adjacent sequences: A085463 A085464 A085465 this_sequence A085467 A085468 A085469
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2003
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 05 2007
Extended by Max Alekseyev (maxale(AT)gmail.com), Sep 15 2009
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