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 A352977 Expansion of e.g.f. cos(2x) cos(3x) / cos(6x) (even powers only). 0
 1, 23, 3985, 1743623, 1424614945, 1870693029623, 3602792061891505, 9566946196183630823, 33500193836861731481665, 149565522713623779723211223, 829235405016410370201483113425, 5589623533324449496004527793434823, 45017811997394066193946619670380594785 (list; graph; refs; listen; history; text; internal format)
 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 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 KEYWORD nonn,easy AUTHOR F. Chapoton, Apr 13 2022 STATUS approved

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Last modified March 26 06:47 EDT 2023. Contains 361529 sequences. (Running on oeis4.)