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A349429 Expansion of e.g.f. cos(5*x)*cos(9*x)/cos(15*x) (even powers only). 4
1, 119, 129361, 353851559, 1806970377121, 14829833979504599, 178506068100424343281, 2962559872323037509279239, 64836735740991992791046187841, 1809194806338763806974577192135479, 62691937652492245112191045131692230801, 2641170468091820745160358034750851940073319 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Only terms of even indices are given. See Formula (10) in the Lawrence-Zagier article.

LINKS

Table of n, a(n) for n=0..11.

Ruth Lawrence and Don Zagier, Modular forms and quantum invariants of 3-manifolds, Asian J. Math. 3 (1999), no. 1, 93-107.

FORMULA

E.g.f.: cos(5*x) * cos(9*x) / cos(15*x).

From Peter Luschny, Nov 17 2021: (Start)

a(n) = (-900)^n*(E(2*n, 1/30) + E(2*n, 11/30)) / 2, where E(n, x) are the Euler polynomials.

a(n) ~ c*(2*n)!*(30/Pi)^(2*n) where c = 0.64812598778325714671749857159... (End)

MAPLE

A349429 := n -> (-900)^n*(euler(2*n, 1/30) + euler(2*n, 11/30)) / 2:

seq(A349429(n), n = 0..11); # Peter Luschny, Nov 17 2021

MATHEMATICA

m = 13; Take[CoefficientList[Series[Cos[5*x]*Cos[9*x]/Cos[15*x], {x, 0, 2*m}], x] * Range[0, 2*m]!, {1, 2*m + 1, 2}] (* Amiram Eldar, Nov 17 2021 *)

PROG

(Sage)

x = PowerSeriesRing(QQ, 'x', default_prec=30).gen()

f = cos(5*x) * cos(9*x) / cos(15*x)

[cf for cf in f.egf_to_ogf() if cf]

CROSSREFS

Sequence in context: A266032 A269123 A336171 * A196429 A243779 A267335

Adjacent sequences:  A349426 A349427 A349428 * A349430 A349431 A349432

KEYWORD

nonn

AUTHOR

F. Chapoton, Nov 17 2021

STATUS

approved

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Last modified May 25 05:58 EDT 2022. Contains 354048 sequences. (Running on oeis4.)