|
%I #18 Feb 24 2023 04:45:11
%S 2,8,32,384,1536,10240,368640,10321920,4587520,297271296,29727129600,
%T 435997900800,15695924428800,116598295756800,1523551064555520,
%U 1371195958099968000,5484783832399872000,41440588955910144000
%N a(n) is the denominator of the polynomial in e^2 giving the (2n)th du Bois Reymond constant.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/duBois-ReymondConstants.html">du Bois-Reymond Constants</a>.
%e {(-7 + e^2)/2, (-25 - 4*e^2 + e^4)/8, (-98 + 3*e^2 - 6*e^4 + e^6)/32}
%p 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
%t 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 *)
%Y Cf. A085467.
%Y Cf. A062545, A062546, A085466, A085467, A138729, A138730, A138731, A138732, A138733.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Jul 01 2003
%E More terms from _R. J. Mathar_, Apr 05 2007
%E Extended by _Max Alekseyev_, Sep 15 2009
|
