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.

1, -6, 360, -45360, 5443200, -359251200, 5884534656000, -35307207936000, 144053408378880000, -1034591578977116160000, 3414152210624483328000000, -471153005066178699264000000, 15434972445968014187888640000000, -926009834675808085127331840000000, 161141112335906068121557401600000000, -6923589032624540122910835317145600000000, 56496486506216247402952416187908096000000000

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

Table of n, a(n) for n=1..17.

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