A262179 - OEIS

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

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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