

A104007


Denominators of coefficients in expansion of x^2*(1exp(2*x))^(2).


3



4, 2, 12, 6, 60, 90, 378, 945, 2700, 9450, 20790, 93555, 116093250, 638512875, 1403325, 18243225, 43418875500, 325641566250, 4585799468250, 38979295480125, 161192575293750, 1531329465290625, 640374140030625, 13447856940643125, 17558223649022306250
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

It appears that a(2n+2) = A002432(n). As A098087(n)/A104007(n) = x*(csch(x)^4)/4*(coth(x)1)^2), then a(2n+2) would represent the sequence of denominators for just the even powers of the full series representation at x=0. A002432 could be conjectured to be the nonhyperbolic, or circle trigonometric, function equivalent where the full series of denominators could be found by the formula x*((csc(x)^2)/4)  cot(x)/2) + 1 for a(n) > 4.
Hyperbolic Trigonometric Functions:
Entire Series: x*(csch(x)^4) / 4*(coth(x)1)^2).
Even Powers: (1/2)*(1x*coth(x)).
Odd Powers: (1/4)*(2x + (csch(x)^2) + 2).
Circular Trigonometric Functions:
Entire Series: x*((csc(x)^2)/4)  cot(x)/2) + 1.
Even Powers: (1/2)*(1x*cot(x)).
Odd Powers: (1/4)*(2x + (csc(x)^2) + 2).
In turn, one may be able to derive some constant for x that can represent the zeta functions of odd positive integers. For zeta functions of even positive integers, that constant is Pi.  Terry D. Grant, Sep 24 2016


LINKS

Table of n, a(n) for n=0..24.


MATHEMATICA

Denominator[ CoefficientList[ Series[x^2*(1  E^(2x))^(2), {x, 0, 33}], x]] (* Robert G. Wilson v, Apr 20 2005 *)


CROSSREFS

See A098087 for further information.
Cf. A002432.
Sequence in context: A243344 A293603 A201825 * A191441 A152664 A167591
Adjacent sequences: A104004 A104005 A104006 * A104008 A104009 A104010


KEYWORD

nonn,frac


AUTHOR

N. J. A. Sloane, Apr 17 2005


STATUS

approved



