A085467 Numerators of coefficients of e^2 in the table of (2n)th du Bois Reymond constants.

0, 1, -7, 1, -4, -25, 1, -6, 3, -98, 3, -24, 36, -8, -1167, 3, -30, 75, -40, -10, -4650, 5, -60, 210, -220, 35, -56, -30930, 45, -630, 2835, -4620, 2205, -378, -1589, -1111860, 315, -5040, 27720, -62160, 52500, -13104, -4424, -36304, -31100895, 35, -630, 4095, -11760, 14700, -6888

Offset

0,3

Links

Table of n, a(n) for n=0..50.

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}.

Mathematica

c[2] = (1/2)*(E^2 - 7); c[n_] := Simplify[ ExpToTrig[ -2*Residue[ x^2/((x^2 + 1)^(n/2)*(Tan[x] - x)), {x, I}] - 3]]; row[n_] := Reverse[ coes = CoefficientList[ c[n], E^2]; coes*LCM @@ Denominator[coes]]; Flatten[ Table[ row[2*n], {n, 1, 9}]] (* Jean-François Alcover, Oct 25 2012, from formula given in A085466 *)

Crossrefs

Cf. A085466.

Sequence in context: A367910 A368184 A086210 * A186168 A117182 A143301

Adjacent sequences: A085464 A085465 A085466 * A085468 A085469 A085470

Keyword

sign,frac,tabl

Author

Eric W. Weisstein, Jul 01 2003

Extensions

Sequence has been prepended with a(0)=0 to enable table display (so offset has been set to 0 accordingly) by Michel Marcus, Sep 11 2013

Status

approved