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A352977
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Expansion of e.g.f. cos(2x) cos(3x) / cos(6x) (even powers only).
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0
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1, 23, 3985, 1743623, 1424614945, 1870693029623, 3602792061891505, 9566946196183630823, 33500193836861731481665, 149565522713623779723211223, 829235405016410370201483113425, 5589623533324449496004527793434823, 45017811997394066193946619670380594785
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OFFSET
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0,2
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COMMENTS
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Only terms of even index are given. Terms of odd index are zero.
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LINKS
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Table of n, a(n) for n=0..12.
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.)
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FORMULA
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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
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MAPLE
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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
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PROG
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(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
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CROSSREFS
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Intermediate case between A002437 and A349429.
Cf. A000192.
Sequence in context: A222031 A233143 A134798 * A308458 A103443 A059000
Adjacent sequences: A352974 A352975 A352976 * A352978 A352979 A352980
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KEYWORD
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nonn,easy
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AUTHOR
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F. Chapoton, Apr 13 2022
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STATUS
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approved
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