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 A280442 Numerators of coefficients in the Taylor series expansion of Sum_{n>=0} exp((-1)^n*euler(2*n)*x^n/(2*n)). 5
 1, 1, 11, 173, 22931, 1319183, 233526463, 29412432709, 39959591850371, 8797116290975003, 4872532317019728133, 1657631603843299234219, 2718086236621937756966743, 1321397724505770800453750299, 1503342018433974345747514544039 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence is related in a peculiar way to A223067, a sequence related to the period T of a simple gravity pendulum for arbitrary amplitudes. See A280443 for more information. LINKS Sergey Khrushchev, Orthogonal Polynomials and Continued Fractions, From Euler's point of view, Corollary 4.26, p. 192, 2008. FORMULA a(n) = numerators of coefficients in the Taylor series expansion of Sum_{n>=0} exp((-1)^n * euler(2*n)*x^n/(2*n)). Let S = Sum_{n>=0} (-1)^n*euler(2*n)*x^n/(2*n) and w(n) = A005187(n) then a(n) = 2^w(n) * [x^n] exp(S). - Peter Luschny, Jan 05 2017 MAPLE nmax:=14: f := series(exp(add((-1)^n*euler(2*n) * x^n/(2*n), n=1..nmax+1)), x=0, nmax+1): for n from 0 to nmax do a(n) := numer(coeff(f, x, n)) od: seq(a(n), n=0..nmax); PROG (Sage) def A280442_list(prec):     P. = PowerSeriesRing(QQ, default_prec=2*prec)     def g(x): return exp(sum((-1)^k*euler_number(2*k)*x^k/(2*k) for k in (1..prec+1)))     R = P(g(x)).coefficients()     d = lambda n: 2^(2*n - sum(n.digits(2)))     return [d(n)*R[n] for n in (0..prec)] print A280442_list(14) # Peter Luschny, Jan 05 2017 CROSSREFS Cf. A046161 (denominators). Cf. A000364 (Euler numbers), A223067, A255881, A280443. Sequence in context: A230604 A161355 A223067 * A218330 A196664 A003729 Adjacent sequences:  A280439 A280440 A280441 * A280443 A280444 A280445 KEYWORD nonn,frac,easy AUTHOR Johannes W. Meijer and Joseph Abate, Jan 03 2017 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)