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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.<x> = 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
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved

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