OFFSET
0,2
COMMENTS
Only terms of even index are given. Terms of odd index are zero.
LINKS
D. Choi, S. Lim and R. C. Rhoades, Mock modular forms and quantum modular forms, Proc. Amer. Math. Soc. 144 (2016), 2337-2349. (See page 2341.)
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices. IV. The Mass Formula, Proc. Roy. Soc. London Ser. A 419 (1988), no. 1857, 259-286. (See table 6.)
M. Monks, Number theoretic properties of generating functions related to Dyson's rank for partitions into distinct parts, Proc. Amer. Math. Soc. 138 (2010), no. 2, 481-494. (See page 485.)
D. Shanks and J. W. Wrench, The calculation of certain Dirichlet series, Math. Comp. 17 (1963), 136-154. (See line 6 of Table 1.)
FORMULA
E.g.f.: cos(2*x) * cos(3*x) / cos(6*x).
From Peter Luschny, Apr 13 2022: (Start)
E.g.f.: (cos(x) + cos(5*x))*sec(6*x) / 2, even powers only.
a(n) = A000192(n)/2. (End)
a(n) ~ 2^(6*n + 3/2) * 3^(2*n + 1/2) * n^(2*n + 1/2) / (Pi^(2*n + 1/2) * exp(2*n)). - Vaclav Kotesovec, Apr 15 2022
MAPLE
egf := (cos(x) + cos(5*x))*sec(6*x) / 2: ser := series(egf, x, 32):
seq(n!*coeff(ser, x , n), n = 0..24, 2); # Peter Luschny, Apr 13 2022
PROG
(Sage)
x = PowerSeriesRing(QQ, 'x', default_prec=30).gen()
f = cos(2*x) * cos(3*x) / cos(6*x)
[cf for cf in f.egf_to_ogf() if cf]
(PARI) my(x='x+O('x^30)); select(x->(x>0), Vec(serlaplace(cos(2*x)*cos(3*x)/cos(6*x)))) \\ Michel Marcus, Apr 13 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
F. Chapoton, Apr 13 2022
STATUS
approved