The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A262179 Signed denominators of the reduced form of the coefficients of degree 2n terms of the Maclaurin series of (t/sinh(t))^x in t. 0
 1, -6, 360, -45360, 5443200, -359251200, 5884534656000, -35307207936000, 144053408378880000, -1034591578977116160000, 3414152210624483328000000, -471153005066178699264000000, 15434972445968014187888640000000, -926009834675808085127331840000000, 161141112335906068121557401600000000, -6923589032624540122910835317145600000000, 56496486506216247402952416187908096000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: this is also the integer sequence A202367 up to sign. These numbers show up in the formula for eigenvectors of Adams operations on the K-theory of unitary groups. LINKS C.-K. Fok, Adams operations on classical compact Lie groups, preprint. EXAMPLE p_n(x):=coefficient of t^{2n} of the Maclaurin series of (t/sinh(t))^x p_0(x)=1 p_1(x)=-x/6 p_2(x)=x(5x+2)/360 p_3(x)=-(35x^3+42x^2+16x)/45360 p_4(x)=175x^4+420x^3+404x^2+144x/5443200 p_5(x)=-(385x^5+1540x^4+2684x^3+2288x^2+768x)/359251200 MATHEMATICA a[n_] := Module[{c}, c = SeriesCoefficient[(t/Sinh[t])^x, {t, 0, 2(n-1)}] // Together; Sign[Numerator[c /. x -> 1]] Denominator[c]]; Table[a[n], {n, 1, 17}] (* Updated by Jean-François Alcover, Feb 15 2019 *) CROSSREFS Cf. A202367. Sequence in context: A002684 A036281 A202367 * A064350 A069945 A086205 Adjacent sequences:  A262176 A262177 A262178 * A262180 A262181 A262182 KEYWORD sign AUTHOR Chi-Kwong Fok, Sep 14 2015 EXTENSIONS Sign added STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 18 05:44 EDT 2021. Contains 343072 sequences. (Running on oeis4.)