OFFSET
0,3
COMMENTS
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
KEYWORD
nonn,frac,easy
AUTHOR
Johannes W. Meijer and Joseph Abate, Jan 03 2017
STATUS
approved