A318142 a(n) = denominator(n!*[z^n]((cosh(x*z) + cos(x*z))*z/(1 - exp(-z)))(1)).

1, 1, 3, 1, 15, 1, 21, 1, 15, 1, 33, 1, 1365, 1, 3, 1, 255, 1, 399, 1, 1155, 1, 69, 1, 1365, 1, 21, 1, 435, 1, 7161, 1, 19635, 1, 21, 1, 959595, 1, 21, 1, 47355, 1, 9933, 1, 2415, 1, 987, 1, 23205, 1, 33, 1, 8745, 1, 4389, 1, 8265, 1, 177, 1, 28393365, 1, 33

Offset

0,3

Links

Table of n, a(n) for n=0..62.

Formula

a(2*n + 1) = 1 for n >= 0.

3 divides a(2*n) for n >= 1.

Maple

gf := (cosh(x*z)+cos(x*z))*z/(1-exp(-z)): ser := series(gf, z, 70):
seq(denom(subs(x=1, n!*coeff(ser, z, n))), n=0..62);

Mathematica

m = 62;
gf = (Cosh[x*z] + Cos[x*z])*z/(1 - E^-z);
Denominator[CoefficientList[(gf/.x->1)+O[z]^(m+1), z]*Range[0, m]!] (* Jean-François Alcover, Jun 04 2019 *)

Crossrefs

Cf. A318141 (numerators).

Sequence in context: A214073 A335265 A141459 * A176727 A080924 A232179

Adjacent sequences: A318139 A318140 A318141 * A318143 A318144 A318145

Keyword

nonn,frac

Author

Peter Luschny, Aug 19 2018

Status

approved