The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Table of n, a(n) for n=0..14. 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 A365034 A196664 Adjacent sequences: A280439 A280440 A280441 * A280443 A280444 A280445 KEYWORD nonn,frac,easy AUTHOR Johannes W. Meijer and Joseph Abate, Jan 03 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 10:56 EDT 2024. Contains 372824 sequences. (Running on oeis4.)